  We consider Einstein's equations coupled to the Euler equations in plane
symmetry, with compact spatial slices and constant mean curvature time. We show
that for a wide variety of equations of state and a large class of initial
data, classical solutions break down in finite time. The key mathematical
result is a new theorem on the breakdown of solutions of systems of balance
laws. We also show that an extension of the solution is possible if the spatial
derivatives of the energy density and the velocity are bounded, indicating that
the breakdown is really due to the formation of shock waves.
