In the framework of algebraic inversion, Magnetic Resonance Elastography (MRE) repeatability, reproducibility and robustness were evaluated on extracted shear velocities (or elastic moduli). The same excitation system was implemented at two sites equipped with clinical MR scanners of 1.5 T and 3 T. A set of four elastic, isotropic, homogeneous calibrated phantoms of distinct elasticity representing the spectrum of liver fibrosis severity was mechanically characterized. The repeatability of the measurements and the reproducibility between the two platforms were found to be excellent with mean coefficients of variations of 1.62 % for the shear velocity mean values and 1.95 % for the associated standard deviations. MRE velocities were robust to the amplitude and pattern variations of the displacement field with virtually no difference between outcomes from both magnets at identical excitation frequencies even when the displacement field amplitude was 6 times smaller. However, MRE outcomes were very sensitive to the number of voxels per wavelength, s, of the recorded displacement field, with relative biases reaching 62 % and precision losing up to a factor 23.5. For both magnetic field strengths, MRE accuracy and precision were largely degraded outside of established conditions of validity (6≲s≲9) resulting in estimated shear velocity values not significantly different between phantoms of increasing elasticity. When fulfilling the spatial sampling conditions, either prospectively in the acquisition or retrospectively before the reconstruction, MRE produced quantitative measurements that allowed to unambiguously discriminate, with infinitesimal p-values, between the phantoms mimicking increasing severity of liver fibrosis.