This work considers the two-dimensional thermoelastic problem in an infinitely long cylinder with free surface subjected to an asymmetrically instantaneous heating on the basis of the generalized thermoelastic theories, i. e. the Lord-Shulman (L-S) and the Green-Lindsay (G-L) theories. The combined forms of the governing equations of both theories are used. The solution in the Laplace transform domain is derived analytically. Using the numerical inversion of Laplace transform has made it possible to obtain the two-dimensional thermal stress and temperature in physical domain for all time scales. Calculations have been performed on the basis of the L-S theory. The behavior of the thermal stress wave is exhibited. The effects of the relaxation time and the thermomechanical coupling on the thermal stress are discussed.