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• A general algorithm for multisurface plasticity is presented. • A general frame to define sequential linear complementarity problem for plasticity. • The set of active constraints is naturally identified by Lemke's algorithm. • Stress is updated using the method of sequential linear complementarity problem. • The robustness of the algorithm is demonstrated via the 3D isoerror map. In this paper, a general algorithm is presented for the integration of multisurface plasticity models. The algorithm combines the return mapping with the technique of the sequential linear complementarity problem (SLCP) to update stress. The set of active constraints is naturally identified by the classical Lemke's algorithm. With the assumptions of isotropic linear elasticity, perfect plasticity, and the associated flow rule, all details are provided in matrix notations to facilitate computer implementation. The extension to hardening/softening multisurface plasticity models is also presented. The application of the algorithm is demonstrated via simulation of three types of geotechnical problems in 2D and 3D. Both linear and nonlinear multisurface plasticity models, e.g. Mohr-Coulomb and generalized Hoek-Brown yield criteria, are examined within the framework of the proposed algorithm. The numerical results are in good agreement with the analytic solutions. Moreover, the accuracy of the proposed stress integration procedure is investigated through 3D isoerror map. The convergence using the consistent tangent matrix at the global level is examined by a one-increment example consisting of one element. [ABSTRACT FROM AUTHOR]