Abstract: In this paper,the dynamic and coupled thermo-elastic problem of a periphery fixed thin rectangular plate with its top surface loaded by a step heat flux was studied.During the process of heat impact, the initial temperature was maintained around the periphery of the plate and its lower surface was assumed to be thermally insulated,The operator method was used to degrade the equation of heat conductivity from three dimensions to two dimensions so that it could match with the two dimensional thermoelastic dynamic equation.Since the two equations were coupled, the dual Fourier series with supplementary terms were used to improve the differentiablity and Laplace transforms were used to eliminate the differential terms to time.Using weighted least squarefi.gtocaTyoutthenuaericalinverseofLaplacetrauforasthesolutionsofprobleasin image space are given,In order to improve the precision of computation and avoid ill-conditioning difficulties of equations,singular value decomposition method was employed to solve the equations by taking advantage of the property of orthogonal transform not leading to the expansion of errors.Finally, the analysis of the effects of the dynamic terms and coupled terms are given.