Changes in the mechanical properties of granular materials, induced by variations in the intrinsic compressibility of the particles, are investigated by means of numerical simulations based on the combination of the Finite Element and Contact Dynamics methods. Assemblies of athermal 2D particles are subjected to quasi-static uni-axial compactions up to packing fractions close to 1. We show that the effect of the compressibility of the particles both on the global and the local stresses, can be described by considering only the packing fraction of the system. This result, demonstrated in the whole range of accessible packing fractions in case of frictionless particles, remains relevant for moderate inter-particles coefficients of friction. The small discrepancies observed with frictional particles originate from irreversible local reorganizations in the system, the later being facilitated by the compressibility of the particles.