The main objective of this work is to reduce the volumetric locking pathology at the Element Free Galerkin (EFG) 3D solid-shell meshless method. For this purpose, a subspace analysis is performed in order to extract the linearly independent incompressible deformation modes that can be reproduced by different background integration cells. Additional deformation modes reproduced by a cell configuration produces more flexibility for the meshless formulation. The Enhanced Assumed Strain (EAS) method is blended with the EFG formulation in such a way that additional (mathematical) variables are included in the formulation increasing its flexibility for nearly incompressible materials. Three numerical examples show the effect of the EAS formulation in alleviating the locking pathology for an almost incompressible material condition. (C) 2012 Elsevier B.V. All rights reserved.