The paper theoretically describes the solid effect in the Si : As structure in ESR conditions at low temperatures and in strong magnetic fields. A quantitative comparison of the results of calculating the dynamic polarization of As nuclei in silicon by the Overhauser mechanism and the solid effect with experimental data has been carried out. A good agreement between theory and experiment was demonstrated and the key parameter of the effects, the time of cross-relaxation transitions, was determined which turned out to be approximately 10 s for the As atom. Keywords: ESR, solid effect, Overhauser effect, flip-flop transitions, silicon.