In most engineering applications, solutions derived from the lower bound theorem of limit analysis are particularly valuable because they provide a safe estimate of the load that will cause collapse. In this paper, the lower bound theorem is firstly implemented making use of the meshless local Petrov-Galerkin (MLPG) method with natural neighbour interpolation. In the present MLPG formulation, the natural neighbour interpolation is employed for constructing trial functions, while the three-node triangular FEM shape function is used as the test function over a local sub-domain. 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 can be generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve these nonlinear programming sub-problems and determine the maximal load amplifier. The numerical results show that the present solution procedure for limit analysis is effective and accurate.