This paper is concerned with the one-dimensional problem of distribution of thermal stresses and temperature in the generalized thermoelastic semispace subjected 10 sudden heating with constant temperature on the bounding plane. The Laplace transform technique is used to solve the problem. The inverse transforms are obtained in an approximate manner as proposed by Paria |19| and Hetnarski |5|. Numerical computations for two particular cases are carried out for small values of lime, and the results are compared with the corresponding solution of the coupled problem obtained by Hetnarski |5|.