  In this paper we study pattern avoidance for affine permutations. In
particular, we show that for a given pattern p, there are only finitely many
affine permutations in $\widetilde{S}_n$ that avoid p if and only if p avoids
the pattern 321. We then count the number of affine permutations that avoid a
given pattern p for each p in S_3, as well as give some conjectures for the
patterns in S_4.
