Abstract The present study shows a parametric analysis of the meshfree method, Element Free Galerkin (EFG), on the elastic analysis of a cantilever beam. This study allows us to determine the best convergence conditions of the solutions varying characteristic. EFG is based on the construction of Moving Least Squares (MLS) approximations using the weighted residual method on the weak formulation, with MLS form functions as the same weighting functions. We consider the parameters of the method such as the order of the basic functions of MLS functions, the size of the support domain of the local MLS functions and the density of Gauss points against errors calculated according to the L 2 norm and processing time. It is shown that by increasing the order of basic functions it is possible to obtain more precise results, however, a larger support diameter and Gauss points higher density are required in order to stabilize the solution, considerably increasing processing times. Therefore, it is only advisable to use high-order base functions when the precision in the results is the priority and a high computational resource is available.