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