At present titanium and its alloys are the most important constructive material in aviation, rocket production and the other area and can be used under high dynamic load that does the actual studies of the behavior of titanium in condition is shock -wave loading. The Experimental studies in given directions were conducted in multiple works. The known that under striking compression of titanium in condition of the moderate temperature occurs its structured conversion. Given work is dedicated to numerical study is shock-wave processes in titanium with provision for polymorphic phase transition and spalling of the destruction. Within the framework of mathematical model porous elastoplastic to models of the ambience is designed numerical methods and program of the calculation for computing experiment, which are safely tested on experimental given on registrations of the profiles to velocities to free surface sample titanium VT5-1. Within the framework of stated models comes to light the inverse conversion at sprain, bring about shaping the shock-waves rarefaction.