Abstract: This paper investigates 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 is established. A direct iteration algorithm is proposed to estimate the shakedown load factor. The difficulties of nonlinearity and nonsmoothness of the objective function are overcome. The convergence of the algorithm is guaranteed. Numerical examples are presented to illustrate the validity of the present method.