Alzheimer's disease is a personally devastating neurodegenerative disorder and a major public health concern. There is an urgent need for medical imaging techniques that better characterize the early stages and monitor the progression of the disease. Magnetic resonance elastography (MRE) is a relatively new and highly sensitive MRI technique that can non-invasively assess tissue microstructural integrity via measurement of brain viscoelastic mechanical properties. For the first time, we use high-resolution MRE methods to conduct a voxel-wise MRE investigation and state-of-the-art post hoc region of interest analysis of the viscoelastic properties of the cerebral cortex in patients with Alzheimer's disease (N = 11) compared with cognitively healthy older adults (N = 12). We replicated previous findings that have reported significant volume and stiffness reductions at the whole-brain level. Significant reductions in volume were also observed in Alzheimer's disease when white matter, cortical grey matter and subcortical grey matter compartments were considered separately; lower stiffness was also observed in white matter and cortical grey matter, but not in subcortical grey matter. Voxel-based morphometry of both cortical and subcortical grey matter revealed localized reductions in volume due to Alzheimer's disease in the hippocampus, fusiform, middle, superior temporal gyri and precuneus. Similarly, voxel-based MRE identified lower stiffness in the middle and superior temporal gyri and precuneus, although the spatial distribution of these effects was not identical to the pattern of volume reduction. Notably, MRE additionally identified stiffness deficits in the operculum and precentral gyrus located within the frontal lobe; regions that did not undergo volume loss identified through voxel-based morphometry. Voxel-based-morphometry and voxel-based MRE results were confirmed by a complementary post hoc region-of-interest approach in native space where the viscoelastic changes remained significant even after statistically controlling for regional volumes. The pattern of reduction in cortical stiffness observed in Alzheimer's disease patients raises the possibility that MRE may provide unique insights regarding the neural mechanisms which underlie the development and progression of the disease. The measured mechanical property changes that we have observed warrant further exploration to investigate the diagnostic usefulness of MRE in cases of Alzheimer's disease and other dementias.