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I plan on applying to law school during the 2013-2014 cycle, and early, as in the Fall of 2013. I will graduate August 2014, which is a few weeks before the Fall semester of law school would start. Would I be uneligible to apply since I will graduate in August? Will my application be at a disadvantage because I wont graduate in May?

You should be fine, most schools will require you to have your Bachelors degree completed by the first day of law school.