Currently, biomechanics of living cells is in the focus of interest due to noticeable capability of such techniques like atomic force microscopy (AFM) to probe cellular properties at the single cell level directly on living cells. The research carried out, so far, delivered data showing, on the one hand, the use of cellular mechanics as a biomarker of various pathological changes, which, on the other hand, reveal relative nature of biomechanics. In the AFM, the elastic properties of living cells are delivered from indentation experiments and described quantitatively by Young’s modulus defined here as a measure of cellular deformability. Here, the AFM studies directly comparing the mechanical properties of normal and cancerous cells are summarized and presented together with a few important issues related to the relativeness of Young’s modulus.