I have asked this question to several astronomers and I’ve never gotten a clear concensus: If the universe is finite and supposedly expanding, then it must have walls or barriers at the points where it ends. First, could a space ship going fast enough hit the outer wall and pop through to the other side. And second, if it could, what would the astronaut find on the other side?
This is a false premise, so any questions proceeding from it are moot. These astronomers you have asked; did they not say there are no walls or barriers?
Perhaps he will become a highwayman again, or he may be a single drop of rain, but he will remain. 
The Earth has a finite surface area and there are no walls or barriers. I think that asking this about the universe is the same sort of thing, but it’s just a lot harder to picture what that means in three dimensions.
Nope. It can be finite and expanding, without walls or barriers.
The simplest analogy/explanation is the surface of a balloon which is being inflated. It is finite and expanding, and the surface area keeps growing, but it still has no end, provided that you keep in mind that we’re talking about the surface of the balloon, not the air inside it. Compare it to a ship traveling the earth’s oceans, going forever without ever reaching any end. Similarly, our universe is curved in a way we cannot see, but it loops back on itself, and one can travel the finite area forever.
You might want to read “A Brief History of the Universe” by Stephen Hawking. It is a fascinating book for the layperson interested in extraterrestrial goings-on, at least as they’re understood by modern human science.
IIRC, Hawking said the universe is finite and folds back upon itself. So if you traveled in a cosmologically straight line long enough, you’d end up where you started.
Then let me reword the question more simply: If the universe is finite, then what is on the other side? For if the universe is finite, then it has to be contained in surrounding space. And hypothetically, if a person were to somehow be transported beyond its boundaries, where, or in what, would that person be?
You really can’t accurately equate the universe to anything that you experience on a daily basis. The universe is unique and defies a proper analogy. Space itself is expanding. It doesn’t need to expand into anything. There is no pan holding the raisin bread.
The finite universe has no sides.
You can not be transported beyond space in exactly the same way you can not go north of the north pole.
Wait… what does God need with a starship?
The universe defines everywhere. There’s no “outside” it. Just because in the normal use of English to describe earthly things words like “finite” and “inside” and “outside” have meaning, doesn’t mean that they are the right words to use to describe the universe.
Unfortunately, the English language is all we laypeople have to describe it, so we end up using these words, even though they’re inaccurate. There aren’t any words we can use instead. And then, having chosen those inaccurate words, people draw conclusions based on the meanings of those words as they’re used to using them.
Your mistake is that you’re attempting to use language created to explain our everyday world, and then derive conclusions from the words you’ve chosen to use. Unfortunately, those words don’t actually adequately describe it, and no conclusion can be drawn from an inadequate choice of words. Our language simply has no real words to describe the universe, so we resort to math to do so.
So physicists describe the universe in math; and it works that way. But when they have to write a popular science book, or explain it to a non-physicist, they have no choice to use silly analogies and English language words. Taking those analogies and words and attempting to extrapolate from them, though, doesn’t work; those analogies and words are just analogies and words, not mathematical models. They don’t actually describe the universe correctly, they just (poorly) attempt to describe concepts which we don’t have the language to describe. You can’t apply logic to them; they’re just poetry, not models.
Heh. Hawking also said in that book that the equations of cosmology work much better if you turn time on its side. I’ve always kind of wondered whether his assertion that his book is for laypeople was a joke on his part, to make us all feel stupid. 
It is likely that the universe is infinite, according to modern cosmologists. Not definite, though.
The acceleration of the expansion of the universe might complicate any attempts to get to the edge of it, even if there were an edge (which no astrophysicist that I know of thinks there is). As might the inflationary period shortly after the Big Bang, when the universe was expanding faster than the speed of light.
Right. Suppose you could travel at the speed of light. You get into your spaceship and head out towards the other side. But the universe is expanding around you, and stuff that’s really far away is expanding away from you faster than the speed of light. So even traveling at the speed of light you will never reach it, even if you had forever.
So there are parts of the universe that you can never reach even at the speed of light, and parts beyond that that you could never even see because light emitted from them can’t reach you even if you travel towards that light at the speed of light.
If the Earth is finite, what happens when you walk over the edge?
Exactly. It’s just words.
Just a random thought. The universe is finite. Or it is infinite. To be honest I can’t quite wrap my head around either one. Though I suppose the finite one is a bit easier to swallow. And that sorta goes for the time aspect of the universe as well. I’ve always thought if I ended up in the looney bin it would be because I developed an OCD and focused on one of these two things (that or where my other half of any sock paired went to).
I am sure there is a branch of physics that proves it is both.