Abstract: The compressible Navier-Stokes equations for an ideal polytropic gas are considered in several space dimensions. The question of possible vacuum formation, an open theoretical problem, is investigated numerically using highly accurate computational methods (pseudospectral in space and high order in time). The flow is assumed to be symmetric about the origin with a purely radial velocity field. The numerical results indicate that there are weak solutions to the Navier-Stokes system in two and three space dimensions which display formation of vacuum when the initial data are discontinuous and sufficiently large. Various tests regarding mass conservation, energy balance, and comparison with the Euler equations suggest that the computed solutions correspond to solutions of the Navier-Stokes system. In addition, in the one-dimensional case, the numerical solutions are also in agreement with recent theoretical results.