In this study, temperature and thermal stress distributions in a steel plate heated from its one side surface under stagnant ambient conditions by a moving heat source are analyzed numerically. Gauss distribution was chosen as a moving heat source profile. While the heat source rotates with a constant angular speed (Omega) around the z axis, the plate moves forward the axial direction. The numerical solutions have been performed for the different thermal conductivity of steel (lambda = 10 to 50 W/m-K) and for the different Omega s of heat source (5 and 10 rpm). Heat source produces the non-uniform steep temperature gradients source due to the fact that the heat flux is subjected on a very small section of the plate.