Limit analysis has been rendered versatile in many structural and metal forming problems. In metal forming analysis, the slip-line method and the upper bound method have filled the role of limit analysis. As a breakthrough of the previous work, a computational approach to limit solutions is considered as the most challenging area. In the present work, a general algorithm for limit solutions of plastic flow is developed with the use of finite element limit analysis. The algorithm deals with a generalized Holder inequality, a duality theorem, and combined smoothing and successive approximation in addition to a general procedure for finite element analysis. The algorithm is robust such that from any initial trial solution, the first iteration falls into a convex set which contains the exact solution(s) of the problem. The idea of the algorithm for limit solutions is extended from rigid/perfectly plastic materials to work-hardening materials by the nature of the limit formulation, which is also robust with numerically stable convergence and highly efficient computing time. (C) 1998 Elsevier Science Ltd. All rights reserved.