The use of mesh free methods, including the EFG method, raises a number of user issues. For the best possible result, the user must choose both the weight function and a series of parameters of the method used. This paper presents a part of the research undertaken by the authors to substantiate, on the basis of numerical experiments, some conclusions that will lead the user as quickly as possible to a more accurate result, which can be validated by analytical results and often by experiment. The numerical experiments performed by the authors are based on the use of their own program, made in Matlab, which allowed the use of many weighting functions, in different conditions established by choosing several values of the internodal distance and the size of the support domain. The numerical experiment is performed on a simple structure, widely used in the technical literature under the name Timoshenko beam, for which there are analytical (exact) solutions for both the displacements and stresses. The obtained results are presented in graphical and tabular form, with the highlighting of the errors compared to the exact solution. The final conclusions provide valuable information for practical work with the EFG method, which are also valid for the use of other meshless methods.