This study presents novel accurate nonlinear buckling solutions of ring-stiffened cylindrical shells. A theoretical model based on the discrete stiffener theory for nonlinear buckling is first developed, which can account for multiple buckling modes, including overall buckling, local buckling, coupled buckling, and tripping. Taking the plate model for a ring stiffener, a ring-stiffened cylindrical shell is partitioned into subshells and circular ring plates according to the ring stiffener positions. With the perturbation technique, the prebuckling and buckling equations of each subshell and ring stiffener in the state space incorporating geometric nonlinearity are derived. The nonlinear state transition equations are transformed into linear equations using the quasi-linearization method, which are then solved using the precise integration method. The state transition equations along with the corresponding constraint conditions are assembled into a global matrix equation to solve for the nonlinear critical buckling loads and mode shapes. Extensive validations of buckling loads, mode shapes, and prebuckling deformations are conducted through comparison with the finite element analysis. The impact of prebuckling nonlinearity on the buckling characteristics of ring-stiffened cylindrical shells is quantitatively investigated, with an in-depth discussion on the effects of ring stiffener number, shell thickness, ring stiffener direction (internal or external), and ring stiffener height.