An equilibrium Element-Free Galerkin (EFG) based formulation for limit analysis of rigid-perfectly plastic plane strain problems is presented. In the formulation pure stress fields are approximated using a moving least squares technique, and a stabilized conforming nodal integration scheme is used in combination with the collocation method, ensuring that the equilibrium equations only need to be fulfilled at the nodes and instability problems can be eliminated. The von Mises yield criterion is enforced by introducing second-order cone constraints, ensuring that the resulting optimization problem can be solved using efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to a benchmark Prandtl problem.