Shear modulus estimation can be confounded by the ill-posed nature of the inverse elasticity problem. In this paper, we report the results of experiments conducted on simulated and gelatin phantoms to investigate the effect of various parameters (i.e., regularization, spatial filtering and the subzone generation process) associated with shear modulus reconstruction on the statistical accuracy (mean squared error), and image quality (i.e., contrast and spatial resolution) of the recovered mechanical properties. The results indicate several interesting observations. Firstly, the intrinsic spatial resolution of magnetic resonance elastography (MRE) is dependent on both regularization and spatial filtering. Secondly, the elastographic contrast-to-noise ratio (CNR_e) increases with increasing regularization and spatial filtering, but it was not affected by the zoning parameters (i.e., the subzones and the extent of the overlap). Thirdly, the statistical accuracy (MSE) of the recovered property improved with increasing regularization, and spatial filtering weight, but the size of the subdomains and their overlap had no significant effect.