The thermal stresses due to a heat source moving crosswise on a finite breadth plate, which is much more like to the practical welding problems, were studied. The temperature distributions in the plate were obtained analytically using the mirror image method, and the thermal stresses were calculated by the finite-difference method. Some numerical calculations for temperature distributions and thermal stresses were performed. The temperature distributions were also obtained by experiment. It was found that the theory was in good agreement with the result of experiment, and the calculated thermal stresses were resonable.