Abstract: In this paper, the general characteristics of the variations of the residual stresses and distortions in the cylindrical shells caused by a single-pass circumferential butt weld are discussed with the use of an approximate calculation method. Special emphasis is put on the analysis of axial bending stress σx which, under certain conditions, may prevail over circumferential stress σθ; and σx reaches a maximum value of σxmax=0.62σ0 at b·β=π/4, and in this case, the value of circumferential stress isσθ=0.33σ0. Within the range of b·β<π/4, σx increases with the value of b·β; and in the range of b·β>π/4, σx decreases with the increase of b·β. Using the functional relations derived by the approximate calculation method, the effects of the geometrical dimensions and the welding conditions on the residual stresses and distortions in cylindrical shells can be inferred directly. These relations coincide with the experimental data and results appearing in cited references.