In this paper, we try to establish a power law for contact resistance versus force Rc = KcFc-n , and we determine via experimental measurements and theoretical calculations, the constants n and Kc in the force range (1 mN-4 N) for bulk metal (Ag, Au, Pd, Ni) used in various applications (microswitches, connectors). The main experimental results of contact resistance are the occurrence of two decrease domains versus progressive load indentation. The first regime corresponds to the earlier touch of the coupon by the probe at force < 0.1 N. This elastic regime evolves to a plastic regime for medium force > 0.1 N. At the transition the exponent value n changes from 0.33 to 0.5 and induce Kc value increasing. Theoretical and computational approaches applied to the elasto-plastic model, confirm the occurrence of these two regimes. Although the calculated values of n are in good agreement with experimental values, some discrepancy between measured and calculated Kc values take place.