The article deals with the creation of a mathematical model that can be applied in the testing of various materials. These are testing cases where the measurement and subsequent evaluation of the value of the coefficient of friction in various tribological measurements is considered. The mathematical model considers the static and dynamic coefficient of friction. It started with the creation of a simpler mathematical model, which was subsequently modified to a more sophisticated one, considering the real situation, which is closer to the real case. With the mathematical model created in this way, various simulations were performed and evaluated for cases of (constant) permanent load, but also repetitive (periodic) load. In another case, an improvement of the mathematical model was carried out, which represented the addition of an option that allows considering the degradation of the investigated material. Degradation of the material represents only part of the surface of the material, which during testing is exposed to contact with another material with a higher hardness than the tested material.