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Recent progress in element technology in large scale explicit finite element codes has opened the way for the solution of elastoplastic shell problems of unprecedented complexity. This new capability has focused attention on the numerical issues involved in the implementation of elastoplastic material models for shells, particularly when vectorizable algorithms are required for supercomputer applications. This paper reviews four algorithms currently in the literature for plane stress and shell plasticity. First, each of the four methods is described in detail. Next, an accuracy analysis is presented for each algorithm for perfectly plastic, linear kinematic hardening, and linear isotropic hardening cases. Finally, a comparison is made of the relative computational efficiency of the four algorithms, and the importance of vectorization is illustrated.