  In this paper we are concerned with the existence of periodic solutions for
semilinear Duffing equations with impulsive effects. Firstly for the autonomous
one, basing on Poincar\'{e}-Birkhoff twist theorem, we prove the existence of
infinitely many periodic solutions. Secondly, as for the nonautonomous case,
the impulse brings us great challenges for the study, and there are only
finitely many periodic solutions, which is quite different from the
corresponding equation without impulses. Here, taking the autonomous one as an
auxiliary equation, we find the relation between these two equations and then
obtain the result also by Poincar\'{e}-Birkhoff twist theorem.
