Mechanical characterization of living cells undergoing substantial external strain promises insights into material properties and functional principles of mechanically active tissues. However, due to the high strains that occur in physiological situations (up to 50%) and the complex structure of living cells, suitable experimental techniques are rare. In this study, we introduce a new system composed of an atomic force microscope (AFM), a cell stretching system based on elastomeric substrates, and light microscopy. With this system, we investigated the influence of mechanical stretch on monolayers of keratinocytes. In repeated indentations at the same location on one particular cell, we found significant stiffening at 25% and 50% strain amplitude. To study the contribution of intermediate filaments, we used a mutant keratinocyte cell line devoid of all keratins. For those cells, we found a softening in comparison to the wild type, which was even more pronounced at higher strain amplitudes.