A technique has been developed for determining coefficients in the power approximation of the “stress–strain” diagram by results of scratch testing with a Berkovich indenter under a normal load of 5 mN on the indenter. The procedure is based on a comparison of experimental results with the finite element simulation of the test process. The technique is intended for application on nanomechanical testing equipment enabling one to perform tests with recording of loading diagrams in terms of the “normal force – indenter displacement” coordinates. To obtain correct results, one must observe the following restrictions: indenter penetration depth > 150 nm under a loading of 5 mN with the indenter tip curvature radius R < 50 nm; indenter penetration depth > 250 nm with 50 < R < 100 nm; the tested metal must be ductile enough, for a scratch to be formed by the mechanism of plastic deformation rather than fracture.