Personally, I do not believe Atlantis ever existed. The oldest known accounts of Atlantis are Critias and Timaeus written by Plato around 360 B.C. Apart from speaking of the origins of man, gods, and an in depth circular discussion of the elements, the stories spoke of the lost city of Atlantis. In this confusing account, many dimensions were given, though never a collective or comprehensive claim as to the size of the whole country. The confusing layout of the city was given and three different sets of dimensions were given on the plain just outside the city. These dimensions are the reason I don't believe there was ever a country or city of Atlantis. Here are the dimensions that are given:
1. "but the country immediately about and surrounding the city was a level plain, itself surrounded by mountains which descended towards the sea; it was smooth and even, and of an oblong shape, extending in one direction three thousand stadia, but across the centre inland it was two thousand stadia." Critias 360 B.C.
2. (speaking of the plain) "It was for the most part rectangular and oblong, and where falling out of the straight line followed the circular ditch. The depth, and width, and length of this ditch were incredible"...."it was carried round the whole of the plain, and was ten thousand stadia in length." Critias 360 B.C.
3. "and the size of a lot was a square of ten stadia each way, and the total number of all the lots was sixty thousand." Critias 360 B.C.
A stadium (plural stadia) is a unit of measurement used by the ancient Greeks and translates to 600 feet. So here are the areas described in square miles (all rounded down):
1. 409,090,909 square miles
2. 5,425,736 square miles
3. 681,818 square miles
Keep in mind that these dimensions are of the area immediately outside the city and thus include neither its size nor the size of the rest of the country. Okay, number 2 is the area inside the cirumference of the ditch which was used for irrigation. That area fits within the earth with no problems, being roughly a little less than twice the size of Australia. However, 1 and 3 are supposed to be the same areas and are very definitely two different figures. Figure 1 is actually quite larger than the entire surface area of the earth (which by the way is 197,379,404.8 square miles rounded down).
Mathematically, Atlantis is impossible by its largest given dimensions and contradictory at best. Not to mention the fact that it was thought up by a culture that was renown for its ability to embellish as well as ineptitude in mathematics (reference the numbers given for the Battle of Thermopylae by the Greeks, which were skewed by a factor of 10).