Abstract: A parameter t is introduced to boundary slip line of rigid regions for plane strain and indirect extrusions with a fractional reduction R=0.5. Integration by substitution has been used along the boundary slip line in order to obtain the extrusion pressure. By the integration depending on a parameter, the following results are obtained, p/2R=1.29 and die pressure is 5.14k for backward extrusion; p/2R=1.29 and pad average pressure is 2.57k for forward extrusion. All the results from this method are the same as those of the conventional solution.

Key words: propagation of wave, transverse isotropy, thermoelastic with voids, isotropic elastic half-space, phase velocity, attenuation coefficient