So there aren't alot of interesting answers here, mostly only boring answers...

Boring answer number 1 is that CS Lewis is writing an adventure story for children, and that the physics and world building of the universe aren't discussed because they aren't of any concern to the goal of telling an adventure story for children.

And boring answer number 2 is that there is no real way to reconcile the physics and geography of a flat earth with any sense of practical reality, because that's why the earth isn't flat.

However.....

If I'm going to make an attempt at a more interesting answer, then I am reasonably convinced that CS Lewis must have based some elements of Voyage of the Dawn Treader on the 14th century Hereford Mappa Mundi (as well as more obvious references from classical mythology such as Homer's Odyssey). It's far too famous an historical artefact for someone with as significant an interest in Medieval literature as CS Lewis to be unaware of.

Anyway, as well as the fact that the map depicts Monopods, Dragons and other such stuff, the geography of the map is one in which Jerusalem is depicted as the centre of a flat world and The Garden of Eden is located across the sea to the East. (East being at the top of the map in this case). If that isn't a spot-on match for Aslan's Country I don't know what is.

Anyway, in this instance the outer sea runs all the way around the edge of the world, with the middle sea (The Mediterranean) being at the centre. So if I'm going to extrapolate the metaphor, I'm going to say that's what happens in Narnia too.

So yes, you could reach the edge of the Narnian continent if you went North, South or West, but like the Garden of Eden on the Mappa Mundi, Aslan's Country is only in the East.

I think you have to look at a map of Narnia to see the geography of what is North, South, and West. 

To the North, is Ettinsmoor, where the giants live. Further is the Wild lands of the North, where Northern Witches have originated. In The Magician's Nephew, Jadis fled far into the North and grew stronger in Dark Magic. After 900 years, she marched back down to Narnia and started the eternal winter (it may be because the north is known for being so cold).

To the west is the wild woods of the West, beyond Lantern Waste. Beyond the Western Mountains is Telmar. Pirates from our world found a secret passageway and settled in Telmar (it's all explained in Prince Caspian).

To the South, beyond the Southern slopes is Archenland, where it has been Narnia's allies since it was first established. Beyond Archenland, further south is the Great Desert, and beyond is Calormen. Narnia had been in diplomatic relations with Calormen since it was established. Most likely Calormen is in the south because the south has been known for heat.

That's what makes Narnia stand out from our own world... our world is round, like a sphere and Narnia is a flat world (people in our world thought the same before the Age of the Exploration). When an author creates another universe, he or she could make a world flat or round like ours if he or she wants to.

Posted by: @wishingtherewasmore

So I've been unable to find any information on what surrounds the continent of this series. I found an awesome map online here that does a great job at detailing the continent, the border's of its nations, and basically everything in it.

That map is a piece of fan fiction — it's interesting, but there are a lot of details around the outer edges (mainly names of extra countries) that were professedly made up by the artist in order to expand Lewis's world further. There's no basis for those in anything written by Lewis himself. As @icarus says, Lewis was writing adventure stories for children and he doesn't bother to take his world-building any further than is needed for the story itself.

So from a canon point of view, the continent that Narnia is on doesn't stretch any further than the maps Lewis gave us in several of the books. Obviously if it were a real world, there would be much more beyond that, but that's purely up to fans' imagination and there's no definitive answer! (Lewis himself, by the way, repeatedly encouraged young readers to write their own Narnia stories, so I would guess he wouldn't at all have minded fans inventing other places and characters beyond the lands he told us about.)

@jasminetarkheena has given you a good description of what we know of the edges of the lands that Lewis told us about. We are of course told in The Voyage of the Dawn Treader that the world of Narnia is flat, although the only physical evidence we're given for that is that at the very edge of the eastern sea, there's a perpetual wave like a wall of water and through it they can just see the mountains of Aslan's Country. We're not told what or where the boundaries of the world are in any other direction.

Posted by: @jasminetarkheena

our world is round, like a sphere and Narnia is a flat world (people in our world thought the same before the Age of the Exploration).

That's not exactly true, by the way, though it's a popular myth. Many educated people knew the world was round from ancient times — the Greek mathematician Eratosthenes calculated the circumference of it in about 240 BC, with surprising accuracy, and later geographers and explorers took their cue from him. On the other hand, some later map-makers, like the cartographer of the Hereford Mappa Mundi, do seem to have assumed that the world was "round like a table" instead of like a ball — or was that just their way of representing a known-to-be-spherical world on a flat surface? It's hard to know exactly what information they were working from, let alone where they got some of their ideas for what kinds of creatures were to be found in distant lands...  

I wrote a series of essays about this on my writer's blog, the links below.

The Odd Geography of the Utter East

The Wild Lands of the North

Calormen and the South

The Western Wild

When I wrote these essays I went by the original text of the British editions.

The gist is: Lewis only hinted at what lay beyond Narnia, if at that. We don't know.

I agree with icarus that Narnia as part of a larger continent surrounded by the sea makes sense.

So does, as I speculate, each cardinal direction having portals into Aslan's country as the magical standing wave in the east serves.

@jasminetarkheena 

This post begins with mention of the continent, and even provides a map with all that you're mentioning. It also says this is about what lies beyond the continent, not in it. Any details you have about what is beyond the continent, to the north, south, and west are appreciated.

@cobalt-jade 

Maybe I wasn't clear in my original post, as everyone seems to be talking about the continent Narnia is on, instead of what the posts is talking about. We all agree about that continent and the general layout of things on it. This post is specifically to discuss what might be in the directions of North, South, and West when leaving the land and going into the ocean. For example, one could say, "I believe that when you go north off the land, you travel 500 km, and hit a perpetual and giant wave, just like in the east." In contrast, one could also say, "I believe that when you go north off the land, you travel 10000 km, and hit a perpetual and giant wave, just like in the east. This would mean that Lewis really meant what he said when he wanted to leave space for others to write their own Narnian adventure in his world, but without being forced to do it on the continent Narnia is on." This is the type of discussion this post was for. Thank you everyone.

Well, the thing is, as much as you... and I... wanted him to, Lewis NEVER specified what was beyond the borders that he set in the book. I've studied these books very carefully, I have all of them on PDFs. Even in the accounts of his life and his writing activities there was never any indication of lands beyond the books (unless there's some secret trove of drawings or writings somewhere that we don't know about.) That map you linked to looks official, but it's just another fan's speculation. I've seen a lot of them. Some adhere to the books and the canon maps while others veer off in different directions entirely.

Lewis was not Tolkien, who mapped everything out, even the places not mentioned in LOTR.

This is one theory about "what lies beyond." This is my own imagination and extrapolates some things from the books.

Now, the continent, of which the land of Narnia is a small part, is surrounded by ocean. The world itself is round and almost flat (there's a slight curve to it like that of a lens), and Narnia, befitting its position as Aslan's first and chosen land, lies approximately at its center, which means the bulk of the oceans are to its east, and unexplored parts of the continent to its west. At each cardinal point of the world, at due east, west, north, and south, there is a way to Aslan's country. In the East there was the standing wave, and there may also be waves in the other points of the compass, or other means of ingress. There is also a way into Aslan's country from the exact center of the world which is where the garden of the silver apples is, and Lewis actually played around with this idea in The Last Battle.

Posted by: @cobalt-jade

I wrote a series of essays about this on my writer's blog, the links below.

The Odd Geography of the Utter East

The Wild Lands of the North

Calormen and the South

The Western Wild

Just wanted to say I really enjoyed reading these, Cobalt Jade! Excellent how you've gone through so many interesting points and hints (and occasional ambiguities and contradictions) all through the books themselves. Thanks for sharing your blog!

(My opinion of Prince Caspian, mind you, is pretty much the opposite of yours, but the world would be a very boring place if everyone always agreed on everything. )

If you keep on going north or south in Narnia would you eventually reach something like our world has in the north and south poles? Narnia is not round like the Earth, but you wonder if it could have something like a pole.   Or is there nothing at the extreme ends of that world in those directions?  I just wondered if Aslan’s country completely surrounds Narnia or if it is just along the eastern edge.  If you go to the extreme west of that world you might not be too far from Aslan since perhaps his country is there too.

So I'm going to stick with my previous theory (that the Narnian continent exists on a flat circular plane, with the ocean going all the way around it, and with the perpetual wave forming a barrier along the entire circumference of the world - and that the entrance to Aslan's Country is only in the east)

... however, I'm also going to add in one further element to my fan theory, which is that the circular ocean is in fact a pool in the Wood Between the Worlds, and that the perpetual wave is some sort of manifestation of the water hitting up against the edge of the woodland pool.

Yes there is obviously a size discrepancy here, but I'm going to wave the "magic" or "quantum mechanics" wand here to explain that away as being some sort of spatio-temporal paradox.

So perhaps then the answer becomes that if they had sailed to edge of the world in any direction other than east, they could potentially have "climbed out" of the Narnia pool and found themselves in the Wood Between the Worlds.

Pure fan theory I know, but I at least like the idea that the physics of Narnia does somehow sit within the framework of the Wood Between the Worlds.