Abstract: Based on the lower bound theorem of shakedown analysis, a solution procedure for shakedown analysis of three-dimensional elastoplastic structures has been established using conventional boundary element method (BEM). The elastic stress field for lower bound shakedown analysis is computed directly by 3-D BEM. The self-equilibrium stress field is constructed by the linear combination of several self-equilibrium stress field is constructed by the linear combination of several self-equilibrium“basis vectors”which can be computed by elastic-plastic incremental iteration of 3-D BEM analysis. The lower bound shakedown analysis problem is finally reduced to a series of nonlinear programming sub-problems with relatively few optimal variables. The complex method is used to solve effectively the nonlinear programming sub-problems. Numerical results show the effectiveness of the present solution algorithm.