a b s t r a c t Shakedown analysis is a powerful tool for assessing the safety of structures under variable repeated loads. By using the element free Galerkin (EFG) method and non-linear programming, a novel numerical solution procedure is developed to perform lower bound shakedown analysis of structures made up of elastoperfectly plastic material. The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration. The reduced-basis technique is adopted here to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. The self-equilibrium stress field is expressed by linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors are generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve the non-linear programming and determine the lower bound of shakedown load. The proposed numerical method is verified by using several numerical examples and the results show good agreement with other available solutions.