Abstract: In this paper, a two-dimensional problem ofmagneto-thermoviscoelasticity with relaxation time in a perfectly conductingmedium is studied. With Laplace transform (for time variable) and Fourier transform(for one space variable), the exact expressions for field quantitiesare obtained in the transformed domain. The resulting formulations are applied toa semi-space problem subjected to ramp-type heating at the surface. Usingnumerical inverse method, the results are obtained and shown graphically when the acrylicplastic material is considered. Also a comparison is made between theresults obtained using the generalized thermoviscoelastic theory andthoseobtained using the conventional thermoviscoelstic theory and thermoelastictheory.