The present work presents the results of mathematical modeling of defo
rmation and thermal processes of compaction of viscous compressible ma
terials. An analytical solution of the problem of one-sided compressio
n and extrusion of powder materials is found which enables us to estab
lish different regimes of compaction and extrusion and to find criteri
al conditions for their realization at a qualitative level. The numeri
cal analysis of the influence of the nonuniformity of the thermal regi
me and the conditions of heat transfer on the regularities of compacti
on nd extrusion of the materials is performed. It is shown how the mod
els developed facilitate the solution of practical problems of produci
ng the concrete items.