The problem of spherical, cylindrical or planar flow of a polutropic gas has been formulated in Lagrangian variables, giving rise to a non-linear second order partial differential equation in two variables, h h and t t . A class of special solutions of this equation has been found by separation of variables, and these solutions depend upon an arbitrary function which is related to the arbitrary entropy distribution in the gas. By specializing this function solutions corresponding to the expansion into a vacuum of an isentropic or non-isentropic gas cloud have been obtained as well as solutions corresponding to the propagation of finite and of strong shocks in variable media.