This paper deals with the limit analysis of rigid perefectly plastic body under the combined action of initial constant loadings and proportional loadings. Using the von Mises yielding condition and the finite element technique, we present an efficient algorithm based on the mathematical programming formula of the classical kinematic theorem of plasticity theory. This algorithm includes an iterative procedure which produces a monotonically decrescent sequence converging to an upper bound of the real limit load. The results of some numerical examples are presented and show the stable convergency of the new algorithm.