Abstract: Finite element nonlinear equations based on Lord-Shulman(L-S) generalized thermoelasticity theory are derived for elastic media withtemperature-dependent properties and solved directly in time domain. A caseof an infinite medium with a cylindrical hole under thermal and mechanicalshock is analyzed with the developed method. The numerical results withtemperature-dependent properties show the fluctuation of heat conduction andthe efficiency of the time domain method in solving generalizedthermoelastic problems. Furthermore, it also shows that the influence oftemperature-dependent properties are more pronounced on mechanical responseof the media with the thermal shock loading, rather than the mechanicalshock.