A technological scheme and computation for the process of stage extrusion in housings of high-strength aluminum alloys are offered. Blank material is assumed to be viscoplastic during hot working, that is, deformation strengthening is followed by softening in view of viscous deformations growth (short-term creep). An extreme theorem of plasticity is used, in accordance with which the deformation kinematics defines the upper boundary assessment of pressure. The flow kinematics is defined with the aid of a discontinuous field of traverse speeds. At the same time a power in the deformation areas and on the surfaces of a speed gap is computed. The pressure of the operation is defined through a power equation of equilibrium in powers and depends upon strengthening and a rate of deformation. The assessment of damageability of blank material is given according to equations of the energetic and kinetic theories of strength at viscoplasticity. The calculated data and a product sample are shown.