The article is devoted to the problem of the origin of the Moon. Discussed modern scenarios for the formation of the Earth-Moon system: simultaneous formation of the Earth and the Moon in the circumsolar gas of dust disk; impact partial destruction of the Earth by a massive asteroid; gravitational capture of the Moon by the Earth; destruction of the double moon at the beginning when approaching the Earth with possible subsequent absorption components of smaller mass by the Earth. We offer two-stage scenario of gravitational capture of the Moon by the Earth in the early stages Solar system. In the first stage, using a hybrid numerical model in the formulation of the three-body problem (Sun, Earth and Moon) and N-bodies, the search and selection of temporary orbits of the Moon around the Earth is carried out. Using the backward integration method in the formulation N-body problem, the influence of tidal forces on pumping of orbital moment of the Moon (\(P_{{{\text{orb}}}}^{M}\)) relative to the Earth at its own moment \(P_{s}^{M}\) is estimated. As the simulation shows, actions tidal forces alone are not enough to capture the Moon by the Earth in a short time time scale \( \sim 100\) years (\(\Delta P_{s}^{M} \sim {{10}^{{ - 6}}}P_{{{\text{orb}}}}^{M}\)). At the second stage, the factor is taken into account viscous-dissipative environment leading to additional “slowing down” of the Moon, due, for example, to collisions with asteroids and the transition of tidal energy into heat, which helps the Moon get rid of excess kinetic energy and gain constant orbit around the Earth.