An analytical method for determination of a stress condition of butt welded thin-gauge plates with asymmetrical reinforcement is developed. The proposed method allows take into account the effect of the load application eccentricity on the tensile stress concentration factor (SCF) in the weld root zone. It is presented that the bending stresses, caused by this eccentricity, result in increasing the total stresses up to 75%. The results of analytical SCF calculations are in good agreement with the results obtained using the finite element method.