The state of stresses in the vicinity of a square hole with rounded corners, including a circular hole as a special case, in a cylindrical shell subjected to axial load is analyzed. The analysis is carried out by two methods, that is, by the theory of shallow shell and the finite element method. The solutions of the Donnelltype equations with singular points at the centers of curvature of rounded corners and some other points, are superposed and the collocation technique is applied to satisfy the boundary conditions. The inflences of the curvature parameter β and the curvatures of the rounded corners of square holes on the state of stresses, especially stress concentrations, are investigated systematically. Several models are analyzed by the finite element method with flat triangular elements and the results are in good agreement with those of the former method except for cases of larger hole.