Normal and tangential forces coexist between rough surfaces in engineering components under most operating conditions. Accurate measurement of contact forces (both normal and tangential forces) on rough surfaces is critical for the safety and stability of engineering equipment, as interfaces are typically discontinuous regions within mechanical systems. However, existing contact mechanics and electrical contact models mostly neglect tangential force effects, hindering their application to shearing behavior research and precluding the development of a contact force measurement methodology applicable to simultaneous normal and tangential force quantification. Inspired by the yield criterion for material damage, a contact mechanics model was developed that simultaneously accounts for the effects of normal and tangential forces. Then, a new principle of contact force measurement is developed by correlating the contact resistance with the real contact area, which enables the simultaneous measurement of normal and tangential forces between rough surfaces based on the single contact resistance under steady-state contact conditions. By proposing a “static friction surface”, the static and dynamic friction stage is effectively differentiated, and the reasons for the sudden drop in friction force and the sudden increase in contact resistance during the static and dynamic transition stages are given. This work proposes a novel explanation for the friction mechanism in terms of mechanical deformation and electrical resistance changes.