Volumetric locking (locking in the incompressible limit) for linear elastic isotropic materials is studied in the context of the Element Free Galerkin method. The modal analysis developed here shows here shows that the number of non-physical locking modes is independent of the dilation parameter (support of the interpolation functions). Thus increasing the dilation parameter does not suppress locking. Nevertheless, an increase in the dilation parameter does reduce the energy associated to the non-physical locking behavior. Although more locking modes are present in the Element Free Galerkin method with quadratic consistency than with the standard biquadratic finite element method. Finally, numerical examples are shown.