A three-dimensional (3D) scratch model is proposed to investigate the effects of yield strength of both coatings and substrates. With the help of combined Coulomb and plastic friction, the obtained results comprehensively interpret the experimental phenomena in most metals that with the growth of hardness after heat treatment the scratch friction coefficient (SFC) increases. This interpretation could not be done before. Scratch tests on the surface with or without the coating are discussed. Without the coating the SFC increases due to the decrease of the area with plastic slippage and/or the increase of friction stress during the increase of the yield strength in the material. With a softer substrate the friction stress decreases but the SFC increases, which is caused by the growth of the entire contact area and surface deformation. Conversely, with a stronger substrate the SFC decreases due to an intensified plastic slippage. The obtained results pave a new way to understanding the effects of yield strength on scratch tests, interpret experimental phenomena, and should be helpful for an optimum design in experiments.