The elastoplastic instability of the symmetrical double-arc ring-stiffened cylindrical shell was analyzed. The critical pressure was obtained for small deflection elastoplastic buckling of the cylindrical shell under hydrostatic pressure. The critical pressure for large deflection buckling of the cylindrical shell with initial geometric imperfections was determined under hydrostatic pressure by using nonlinear large deformation theory. The effects of hoop equivalent wave number, initial geometric imperfection and the central angle of circular arc on buckling mode and critical pressure of double-arc ring-stiffened cylindrical shell were analyzed. The results showed that the hoop equivalent wave number of arc cylindrical shell had an main effect on the critical pressure of the structure, designed equivalent hoop wave number of double-arc cylindrical shell should not be approach to the hoop wave number corresponding to minimum critical pressure, and the central angle of circular arc had less effect on critical pressure of the structure.