This paper is one of our studies on the problem of thermal stress and residual stress due to welding. Weld stress problem must be cansidered from the standpoint of thermo-elastico plasticity, but it is very difficult for the case of thermal stress due to moving electrode. In this paper, therefore, we have made, for the first step, the elastic study on the problem of plane thermal stress due to moving heat source. We extended at first a general theory of thermal stress due to moving heat source, and as blem of straightly moving point heat source with a constant speed in an infinitely large plate. Further we discussed on the principal stress in quasi-stationary state and the effect of high temperature region near the heat source on the distribution of thermal stress.