The ability of cells to sustain mechanical stress is largely modulated by the cytoskeleton. We present a new application of optical tweezers to study cell's mechanical properties. We trap a fibronectin-coated bead attached to an adherent H4II-EC3 rat hepatoma cell in order to apply the force to the cell surface membrane. The bead position corresponding to the cell's local mechanical response at focal adhesions is measured with a quadrant detector. We assessed the cell response by tracking the evolution of the equilibrium force for 40 cells selected at random and selected a temporal window to assess the cell initial force expression at focal adhesions. The mean value of the force within this time window over 40 randomly selected bead/cell bounds was 52.3 pN. Then, we assessed the responses of the cells with modulation of the cytoskeletons, namely the ubiquitous actin-microfilaments and microtubules, plus the differentiation-dependent keratin intermediate filaments. Notably, a destabilization of the first two networks led to around 50 and 30% reductions in the mean equilibrium forces, respectively, relative to untreated cells, whereas a loss of the third one yielded a 25% increase. The differences in the forces from untreated and treated cells are resolved by the optical tweezers experiment.