A semi-submersible ship is composed of three parts ; a superstructure, lower-hulls, and columns. Stiffened cylindrical shells are used as columns in order to decrease structural weight. Most of these cylindrical shells have several axial stiffeners connected with girders of a superstructure and/or with rings of a lower-hull. The local collapse of stiffeners under concentrated axial compression load transmitted through girders or rings often becomes one of the most important problems of those structures. This paper presents a simplified method for estimating the collapse loads of stiffeners which are axially connected with cylindrical shells and are subjected to concentrated axial compression load. Two kinds of collapse mode are considered, i) plastic collapse, and ii) collapse after elastic buckling. In the case i), the collapse loads are defined by the effective width of cylindrical shells obtained from experimental results, and in the case ii), effective lower-bound solution of buckling load is obtained by a simplified equation.