The time-dependent, compressible extrusion of a Carreau fluid is solved over the reservoir-die-extrudate region using finite elements in space and a fully implicit scheme in time. A nonmonotonic slip law based on experimental data on polyethylene melts is assumed to hold along the die wall and the velocity at the entrance of the reservoir is taken to be fixed and uniform. As in the case of the extrudate-swell flow, the combination of compressibility and nonlinear slip leads to self-sustained oscillations of the pressure drop and of the mass flow rate in the unstable regime. The effects of the reservoir volume, the imposed flow rate, and the capillary length on the amplitude and the frequency of the pressure and free surface oscillations are studied and comparisons are made with experimental observations. (C) 2006 Elsevier B.V. All rights reserved.