Abstract: Investigated the computational shakedown analysis of an elastic-perfectly plastic body subjected to a set of loads varying within a given domain. Using von Mises yield criterion and finite element technique, a mathematical programming formulation for kinematic shakedown analysis was established. A direct iteration algorithm was proposed to estimate the shakedown load factor. The difficulties of nonlinearity and non-smoothness of the objective function were overcome. The results show that the algorithm has higher accuracy and efficiency, the convergence is guaranteed. Numerical examples are presented to illustrate the validity of the present method.