Many molecular and cellular pathogenic mechanisms of neurodegenerative diseases have been revealed. However, it is unclear what role a putatively impaired neuronal transport with respect to altered mechanical properties of neurons play in the initiation and progression of such diseases. The biochemical aspects of intracellular axonal transport, which is important for molecular movements through the cytoplasm, e.g., mitochondrial movement, has already been studied. Interestingly, transport deficiencies are associated with the emergence of the affliction and potentially linked to disease transmission. Transport along the axon depends on the normal function of the neuronal cytoskeleton, which is also a major contributor to neuronal mechanical properties. By contrast, little attention has been paid to the mechanical properties of neurons and axons impaired by neurodegeneration, and of membraneless, phase-separated organelles such as stress granules (SGs) within neurons. Mechanical changes may indicate cytoskeleton reorganization and function, and thus give information about the transport and other system impairment. Nowadays, several techniques to investigate cellular mechanical properties are available. In this review, we discuss how select biophysical methods to probe material properties could contribute to the general understanding of mechanisms underlying neurodegenerative diseases.