This paper was aimed at reviewing the theory and numerical implementations of the natural elements method (NEM, meshless method) used for resolving structural problems. An exact analytical solution and the finite element method were used for comparing the results obtained for two lineal-elastic structural problems in two spatial dimensions. The interpolation procedure used by the method for obtaining the trial functions and the most important features of the standard NEM are described. The results of two simulations concerning structural problems are presented using a code written in Matlab 6.5 for resolving differential lineal elasticity equations in two dimensional domains it was found that NEM is similar to the finite element method in terms of stability and convergence, having the advantage of mesh being automatically produced and the approximated solution not depending on the distribution of the node cloud, thereby defining the geometric domain.