In designing offshore structures and ships including LNG carrieres, it is very important to accurately predict the buckling strength and collapse strength of stringer stiffened cylinders under axial compression, expecially with initial imperfections. Some researches have been reported with respect to the elastic buckling strength of stringer stiffened cylinders with initial imperfections, but there still remain unknowns because the characteristic of buckling strength is much affected by many shape parameters for example Batdorf parameter Z, the size of stiffeners and the eccentricity of applied load. Moreover, there are few systematical numerical researches in the plastic range. This paper introduces the resultant force method (FEM), which was developed by authors, to the elasto-plastic analysis of stringer stiffened shells, and moreover investigates effects of the initial imperfections on the collapse strength of stringer stiffened cylinders under axial compression. Main conclusions obtained from this study are as follows : (1) The usefulness and accuracy of the resultant force method are confirmed by comparison with the experimental results and other numerical results. (2) Effects of initial imperfections on the buckling strength of stringer stiffened cylinders, not only in the elastic range but also in the plastic range, have been presented. (3) In the elastic range, the stiffened cylinders with Z >75 when A_s/d_st =0.1 or with Z >200 when A_s/d_st =0.2 are very sensitive to imperfections and buckle with asymmetric mode. On the other hand, the heavy stiffened cylinders with short length are not so sensitive to imperfections and buckle with axisymmetric mode. (4) In the plastic range, the more plastically the stiffened cylinders collapse, the smaller the effects of the imperfections on the collapse load become.