The subject of this paper is to study the thermoelastic behavior of a functionally graded semi-infinite medium heated uniformly by a laser beam having temporally Gaussian distribution. The surface of the medium is taken as traction free. The general solution is obtained in the Laplace transform domain. The inverse of the Laplace transform is computed numerically using the Riemann-sum approximation method. The numerical results for temperature, displacement and stress are obtained and presented graphically for the generalized theory of thermo-elasticity with one relaxation time.