The Ark was a very large ship. It would have been larger than any other wooden ship ever constructed by humans.
But as large as it was, it wouldn’t have come close to being large enough to handle all of the different animals that live on Earth.
One problem is that there is no consistent count of the animals on the Ark.
There are millions of different species of animals on Earth. New ones are being found every day. Moreover if currently extinct species such as dinosaurs were included on the Ark (as many creationists contend) that number goes up by a couple of orders of magnitude.
Even if you don’t include insects, the most literal of Biblical literalists seems to agree that two of all animals couldn’t have fit onto the Ark. Their explanation for how it all was accomplished may surprise you: after the Ark, the diversity of life that we see was created through evolution!
In 1996, a creationist who uses the pseudonym John Woodmorappe, was hired by the Institute for Creation Research to write a book explaining away the problems with the flood story in the Bible. The resulting book is titled Noah's ark: A feasibility study.
Woodmorappe recognized that even a ship as large as the Ark couldn’t have carried two of every species of animal. He hypothesized that only “kinds” of animals came on board. Then after the Ark came to rest, those “kinds” of animals evolved into the many different species that we see today.
There was, for example, a “cat” kind on board the Ark which, after the Flood, evolved into lions, tigers, panthers, leopards, mountain lions, domestic cats, etc.
That hypothesis certainly drastically cuts down on the number of animals on board the Ark. But there are still problems.
First of all, there is no definition of the word “kind” that has any biological meaning.
Secondarily, such rapid evolution has never been witnessed! Even though the exact date for the flood has never been pinpointed because of the conflicting evidence, no creationist claims that it happened more than a few thousand years ago. Did all cat species evolve from an original “kind” prototype in such a short time?
In fact, the time required for that evolution is really just a few centuries at most. That’s because we don’t still see such rapid evolution. In the last few centuries since scientists have been paying particularly close attention, there have been zero new species of cats produced in nature. So if that rapid evolution took place, it must have completed in a millennium or so and then, for some reason, suddenly stopped!
Explanations for this rapid evolution followed by evolutionary stasis are lacking.
Finally, even this smaller number of animals is problematic. Scientists have analyzed Woodmorappe’s figures and concluded that 15,746 animals weighing between 411,902 and 5,463,694 kg (906,000 to about 12 million pounds) – depending on the percentages of juveniles and adults - were on the Ark.
Then we have to consider the food requirements. Some animals with a high metabolic rate, likes shrews, can eat three times their own body weight per day! Though they are small, a year's worth of food for them is significant. Even cold-blooded reptiles will eat more than their own body weight in a year. If all of those things are added together there simply isn’t room for all of those animals and the food and other supplies needed for them.
 http://www.talkorigins.org/faqs/faq-noahs-ark.html, referenced on May 8, 2008