  We investigate the rotation sets of billiards on the $m$-dimensional torus
with one small convex obstacle and in the square with one small convex
obstacle. In the first case the displacement function, whose averages we
consider, measures the change of the position of a point in the universal
covering of the torus (that is, in the Euclidean space), in the second case it
measures the rotation around the obstacle. A substantial part of the rotation
set has usual strong properties of rotation sets.
