A phase field model accounting for inhomogeneous and anisotropic elasticity has been used to investigate the consequences of inhomo- geneous elasticity on the formation and coarsening of cuboidal microstructures in Ni-based superalloys. For that purpose, two- and three-dimensional calculations have been carried out considering high volume fractions of gamma' precipitates, and accounting for their ordered crystal structure. The analysis of a substantial number of cases with different contrasts of elastic constants highlights the primary role played by the inho- mogeneity Delta C' of the shear modulus C' on the shapes and spatial arrangements of the precipitates. This can be attributed to the sensitivity of the mechanisms involved in coarsening to Delta C'. Finally, scanning electron micrographs of the AM1 superalloy are statistically analyzed and discussed in light of the calculations.