A numerical algorithm for plane stress and shell elasto-plasticity is presented in this paper. The proposed strain decomposition (SD) algorithm is an elastic predictor/plastic corrector algorithm, and in the context of operator splitting, is a return mapping algorithm. However, it differs significantly from other return mapping algorithms in that only the necessary response functions are used without invoking their gradients, and the stress increment is updated only at the end of the time step. This makes the proposed SD algorithm more suitable for materials with complex yield surfaces and will guard against error accumulation during the time step. Comparative analyses of structural systems using the proposed strain decomposition (SD) algorithm and the iterative radial return (IRR) algorithm are presented. The results demonstrate the accuracy and usefulness of the proposed algorithm.