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The static shakedown theorem was reformulated for the boundary element method (BEM) rather than the finite element method with Melarrs theorem, then used to develop a numerical solution procedure for shakedown analysis. The self-equil ibrium stress field was constructed by a linear combination of several basis self-equilibri um stress fields with undeterm ned pararreters. These basis self-equili brium stress fields were expressed as elastic responses of the body to imposed permanent strains obtained using a 3-D BEM elastic-plastic increrrental analysis. The lower bound for the shakedown load was obtained from a series of nonlinear rrathematical proqramrning problems solved using the Complex method. Numerical examples verified the precision of the present method.