Animal cells crawl in tissue to achieve their functions. The cell locomotion is a typical case of collective phenomena in biological systems. By atomic force microscopy (AFM), we measured the spatial distribution of local elasticity over cells of fibroblasts, which are kept alive in physiological conditions. The AFM experiments revealed that: (1) the nucleus area of the cell surface is about 10 times softer than the surroundings, and (2) distribution of local elasticity is evolving in time. The drug-dosing experiments confirm that the cell shape and stiffness originate mainly in actin filaments but not in microtubules. The elasticity pattern does not always correspond to that of actin filaments from fluorescence observations. These results indicate that the cell stiffness results not only from the density of actin filaments but also from their dynamical properties.