  It is shown that the initial singularities in spatially compact spacetimes
with spherical, plane or hyperbolic symmetry admitting a compact constant mean
curvature hypersurface are crushing singularities when the matter content of
spacetime is described by the Vlasov equation (collisionless matter) or the
wave equation (massless scalar field). In the spherically symmetric case it is
further shown that if the spacetime admits a maximal slice then there are
crushing singularities both in the past and in the future. The essential
properties of the matter models chosen are that their energy-momentum tensors
satisfy certain inequalities and that they do not develop singularities in a
given regular background spacetime.
