  In this paper we study the ergodic properties of mathematical billiards
describing the uniform motion of a point in a flat torus from which finitely
many, pairwise disjoint, tubular neighborhoods of translated subtori (the so
called cylindric scatterers) have been removed. We prove that every such system
is ergodic (actually, a Bernoulli flow), unless a simple geometric obstacle for
the ergodicity is present.
