The article describes the mathematical model of a hydraulic support system of the powered support sections with impulse-free continuous regulation of its resistance to the roof rock lowering. Safety valves of the hydraulic support perform only protective functions. Mathematical modeling was carried out using the Runge-Kutta method and the Wolfram Mathematica computer algebra system. The results of modeling the transient process of the hydraulic support system with a built-in block for regulating its resistance during impulse loading of the support section with a collapsed roof rock block at "Polosukhinskaya" mine are presented.