Heavy duty by-pass switches, consisting of canted coil spring structure, are indispensable in power electrical connection application with low contact resistance. Minimizing the contact resistance is a major issue in service reliability, which has been extensively investigated in the literature. The calculation of contact resistance is a very complicated process because of the determination of insertion force and resulted multiple irregular mechanical contact spots. In this work, an analytical model of the insertion force, contact force, contact area and contact resistance was developed. The results obtained from the proposed model were compared against those typically obtained from commercial FEA software COMSOL Multiphysics. The calculated insertion force agreed well with FEA, while the analytical model was more than five orders of magnitude faster. The proposed calculation method is beneficial for the canted coil spring design regarding the heavy duty by-pass switches.