This is one of those subjects that always dismays me. Not so much because they believe in the Flood, but that they believe in the flood so thoroughly, despite all the evidence to show that this is not the case.
Before I start, the only other article on here talks about the geological evidence that there was a flood. At worst, this is an outright lie, at best, misguided ignorance. There's no physical record, geological or otherwise, of any kind of global flood within recorded human history. There wouldn't even be an interpretable geological record this recent; geology deals in epochs spanning millions of years, if not billions. There's records of catastophes, yes. The Permian extinctions spring to mind, and the KT impact. But these are so far back that any ancestors of the writers of the Bible would have been small shrewlike protomammals. They may have kept records at the time, but we've yet to discover any.
So, on to the problems. Firstly, there's just not enough water for a global flood, and never has been. Every raincloud in the sky at the moment, if compressed together, would account for around 3% of the world's total freshwater. Some claim the Flood was due to some kind of global warming type event, where the icecaps melted. Again, all well and good, unless you actually look at the figures. If both caps totally melted, it'd raise the average sea level by around 250-300 feet. That's not enough to cover a modest hill, let alone every mountain range in the Middle East, or the world.
But, it's God we're talking about here, so we're going to have to make allowances. No doubt he could have magically conjured perhaps 20-30 times the total amount of water in the world at present to cover the whole planet, and also make sure it went away again after 40 days. You have to assume these sort of things if you're going to take appropriated myths literally.
So, we have a planet completely covered with water. All the sinful people drown (and presumably all the sinful animals too, as God can be much more specific with his wrath when he wants to be. Presumably, as Eddie Izzard wondered, evil ducks, geese, and other waterfowl survived, and their descendants will take over the world before long). But not everyone dies, because God got Noah to build a boat, and gather a handful of his family and two of every animal onto it.
You know where I'm going with this. But two minor asides first. We get very exacting measurements for the size of the Ark in the Bible. Without going into specifics, it's a large boat. But it'd comfortably fit into the hold of a supertanker nowadays. It's big, but it's not big enough.
Secondly, when the waters recede, there's perhaps three or four breeding pairs of humans left on the planet (depending on whether noah's wife was capable of bearing children still). We know how inbreeding works, and this isn't a sufficiently large gene pool. If we'd all descended from such a small population, there wouldn't be a person in the world who had anything resembling a chin.
And then, of course, there's the problem you've all been waiting for. Two of every kind. That's EVERY kind. All on one ship together. This is ridiculous on so many levels, it's hard to know where to begin. Did Noah gather the lemurs, marsupials and other creatures only indigenous to places like Mauritius and Australia before the rains started? Did he have room for the 350,000 species of beetle that exist, and the several million other species of insect around the world? And these are only the known species, I might add. New ones are discovered on a regular basis. And I'm not even looking at anything that's developed beyond having an exoskeleton.
And presumably there were all the carnivores on board. Lions, tigers and bears, oh my. For forty days. Did Noah bring extra sheep to feed them? And fodder for the herbivores? Or is this why we don't have unicorns and griffons and the like nowadays: The wolves ate them?
Now, bear in mind, I've not even begun to touch upon the problems with taking this story as true. I've covered the physical impossibilities for those who like to think the story was an allegory, or has some root in truth. It doesn't, I'm afraid. What I haven't even touched upon are the problems of the story being stolen wholesale for a dozen other mythologies, which make even its worth as an allegory even more unlikely.
Asking whether there was a global flood is like asking whether there really was a magic beanstalk that reached up to the clouds.