This study aims to analyze the strength of pressure hull of a small submarine. The pressure hull of a submarine has to withstand very large differential pressure between hydrostatic pressure in submarine operating depth and atmospheric pressure in inner space of a submarine. To do that, the pressure hull is generally ring-stiffened cylindrical shell under external pressure. In this situation, there are some foreseeable failure modes of the pressure hull such as shell yielding, axisymmetric shell buckling, asymmetric shell buckling, overall buckling and buckling of end closure. We calculated collapse pressures of these failure modes with approximation and empirical formulas. And, to analyze critical buckling pressure, we performed eigenvalue analysis with finite element method tools.