In automobile frame work, box members formed by spot welding two thin walled members of hat section together, or by welding a flat plate to one hat member are widely used as members. (The former are called double hat members, and the latter single hat members.)When such members are subjected to repeated torsion, cracks would occur at the spot weld point. This is due to a large shearing force transmitted through the weld point. Since fatigue strength is directly required in the aspect of design, many studies are being made in this connection. Considering that the basis of fatigue strength is primarily the stress distribution around the weld point, its problem must be clarified by all means.In this report, then, the stress distribution of welding flanges was theoretically analyzed as a plane stress problem and a bending problem of plates by the theory of elasticity and obtained by superposition of these solutions. These theoretical results were compared with results of the finite element method and with the experimental results.