It is very important to note that there is no evidence for a global flood ever taking place on earth. A global flood would have left evidence of changes to the ice cores in Greenland, destroyed the polar ice caps, left traces on the sea floor and we would not have had tree records dating back to more than 10 000 years. Please see here for more information on this. In addition, for all the land mass to be covered by water, we would need three times as much water as there currently resides on earth, including all the oceans and the polar caps.
In order to get around this problem, Christian and Jewish apologetics argue that it was not a global flood but a local flood. If it was a local flood, then surely there has to be some geological or archaeological evidence for such a catastrophic event. So how much evidence is there for this event?
Firstly the Bible dates the flood to 1300 before the building of the first temple. The first temple was build around 950 BCE and as such the flood had to take place around 2500 BCE. The first thing we notice about this event is that none of Israel's neighbours recorded a flood at this time even though they were producing vast amounts of literature. The pyramids themselves were being built 300 hundred years before the flood took place. There is no evidence for a reduction in the amount of animals or even the human populations in this area at this stage. In fact there is no archaeological evidence at all for this event taking place in this region at this time outside of the Bible.
Norman Cohn in his book "Noah's Flood: The Genesis story in Western thought" states that over 300 cultures have records of a major flood. The most well known of these is the Epic of Gilgamesh which came from the Assyrians. In this story Ut-Napishtim is chosen by the Babylonian god Ea (the Babylonian version of El) to build an ark in order to save a select group of humans and animals. There are over twenty similarities between these two stories and they can be viewed here. It is worth noting that it the Epic of Gilgamesh is generally considered to be the first work of literature. It also provides a date between 2500 and 1700 BCE for this flood and it has been proposed that the Israelites adopted this Babylonian story when they were slaves in Babylon in the 6th century BCE. Because there are so many similar flood stories in this region, there must be some origin for this story.
William Ryan and Walter Pitman, both senior scientists at Columbia University, have developed a theory that Noah's flood was actually based on a catastrophic even in 5600 BCE. They found that the banks of the Black Sea burst and 60 000 square miles of land were covered in water in less than a year. They state that the force of the rushing water would have been 200 times that of the Niagra falls and this would have looked like the wrath of an angry god to the local people. Their theory is further supported by the National Geographic Society who discovered well preserved human artefacts at the bottom of the Black Sea as well as further findings by the Assemblage - Noah Project and Mark Siddall.
They also theorize that the local inhabitants fled the area and went on to settle in various neighbouring regions including Eastern and Western Europe, Egypt and Central Asia, taking with them the story of the flood and an angry god. A few thousand years later this story had been passed on from generation to generation, growing and changing until it became the Epic of Gilgamesh later adopted by the Hebrews when their religious texts were written between the 8th and 6th BCE.
It's also worth noting that it is not uncommon for flooding to occur and people in the past to have invented religious explanations for natural phenomena. People still do it today. If you take earthquakes for example, we have records of mythical beliefs related to earthquakes dating back thousands of years. These records come from India, South America, East and West Africa, Romania, Scandinavia and New Zealand. Does this mean that there was a single giant earthquake that shook the entire planet? Of course not.
These records include the belief that a giant fish carries a stone on his back. A cow is standing on the stone whilst balancing the planet Earth on one of his horns. After a while the cow's neck begins to ache and he tosses Earth from one horn to the other and it is this juggling act which causes earthquakes.
This is of course ridiculous, but why is it any more ridiculous than believing that a god instructed a man to build a gigantic boat to save all the animal species on the planet, while it rained so much that the entire planet was under water for forty days and forty nights...