Grain-scale characteristics and formation history determine spatial variability in granular masses. We investigate the effect of spatially varying stiffness on the load-deformation response under zero-lateral strain conditions using numerical simulations of correlated random fields, where the granular medium is represented by a non-linear stress-dependent meso-scale model. Results show that stiffness heterogeneity results in higher global compressibility as compared to the homogeneous medium with the same arithmetic mean stiffness. Furthermore, the non-homogeneous stress field that develops inside the granular mass is characterized by focused load transfer along columnar regions, higher stress anisotropy and lower horizontal-to-vertical stress ratio K0 than in a granular medium of homogenous stiffness. As the applied stress increases, the inherent stress-dependent response of the granular material leads to a more homogenous stress field. While greater variance in stiffness causes lower global stiffness, a longer correlation length results in greater variance in global mechanical response among multiple realizations.