Atomic force microscopy is a common technique used to determine the elastic properties of living cells. It furnishes the relative Young's modulus, which is typically determined for indentation depths within the range 300-500 nm. Here, we present the results of depth-sensing analysis of the mechanical properties of living fibroblasts measured under physiological conditions. Distributions of the Young's moduli were obtained for all studied cells and for every cell. The results show that for small indentation depths, histograms of the relative values of the Young's modulus described the regions rich in the network of actin filaments. For large indentation depths, the overall stiffness of a whole cell was obtained, which was accompanied by a decrease of the modulus value. In conclusion, the results enable us to describe the non-homogeneity of the cell cytoskeleton, particularly, its contribution linked to actin filaments located beneath the cell membrane. Preliminary results showing a potential application to improve the detection of cancerous cells, have been presented for melanoma cell lines.