The axisymmetric extrusion process of fully dense metal and sintered powder metal materials is analysed in the present paper. The fully dense metal is taken to be rigid-perfectly-plastic, which also obeys von Mises yield criterion, while Gurson's plasticity is used to simulate the constitutive behaviour of the sintered powder metal. Siebel's model is adopted to take account of the friction forces at the die—workpiece interface. Assuming that the axisymmetric die tapers slowly down the extruding axis, the fundamental governing equations are solved by using a regular perturbation method. This leads to asymptotic expressions of the velocity components, stress components and porosity in the metal material workpiece. Two numerical examples are finally given to show the variations of the field variables with die parameters.