Mathematical models of dynamic compaction and extrusion of incompact metallic m aterials are considered. According to the model of dynamic compaction, irreversible material volume changes occurring under the shock action are considered on the basis of the general equations of mass, momentum and energy conservation, which are written for the d iscontinuity surface. A mathematical model of impact extrusion of incompact wire stock through a conical die is proposed. It is based on the superposition of the solutions of two problems, namely, compaction of powder material in a cylindrical press mold and impact extrusion of an incompressible material. The model allows one to determine the minimum tool velocity required to perform extrusion.