This　paper　presents　an　investigation　of　temperature,　displacement,　stress,　and　induced　magnetic　field　in　a　half　space　perfectly-conductive　plate.　Finite　element　equations　regarding　generalized　magneto-thermoelasticity　problems　with　two　relaxation　times　(i.e.,　the　G-L　theory)　are　derived　using　the　principle　of　virtual　work.　For　avoiding　numerical　complication　involved　in　inverse　Laplace　and　Fourier　transformation　and　low　precision　thereof,　the　equations　are　solved　directly　in　time-domain.　As　a　numerical　example,　the　derived　equation　is　used　to　investigate　the　generalized　magneto-thermoelastic　behavior　of　a　semi-infinite　plate　under　magnetic　field　and　subjecting　to　a　thermal　shock　loading.　The　results　demonstrate　that　FEM　can　faithfully　predict　the　deformation　of　the　plate　and　the　induced　magnetic　field,　and　most　importantly　can　reveal　the　sophisticated　second　sound　effect　of　heat　conduction　in　two-dimensional　generalized　thermoelastic　solids,　which　is　usually　difficult　to　model　by　routine　transformation　methods.　A　peak　can　be　observed　in　the　distribution　of　stress　and　induced　magnetic　field　at　the　heat　wave　front　and　the　magnitude　of　the　peak　decreases　with　time,　which　can　not　be　obtained　by　transformation　methods.　The　new　method　can　also　be　used　to　study　generalized　piezo-thermoelastic　problems.