The kinetics of stress-induced degradation of a star polymer additive dissolved in a mineral oil lubricant was modeled. Polymer degradation was modeled based on a new system of kinetic integrodifferential equations for the distribution densities of star polymer molecules with different numbers of arms and arm chain lengths. Some properties of the solution were established. A numerical method for solution of the problem was proposed and realized. Some of the numerically simulated molecular weight distributions were compared with the independently obtained experimental ones. The lubricant viscosity losses due to polymer degradation were determined and compared with the experimentally measured ones. The theoretical and experimental data are in very good agreement.