Abstract: In this paper, mathematical modeling of the suspension flow in a complex system offractures, when the main fracture is crossed by the secondary one, is carried out. Themathematical model of the process is constructed in the one-fluid approximation and includes thecontinuity equation for the suspension, the system of equations of suspension motion, and themass conservation equation in the form of a convective—diffusion transfer equation for the volumeconcentration of particles. The solution to the problem in a 3D formulation is implemented in theOpenFOAM software package. Thedynamics of the distribution of solid spherical particles in the network of fractures is studieddepending on the ratio of the characteristic Reynolds numbers for the flow and particles, as well ason the ratio of the lengths of the main and secondary fractures. © 2023, Pleiades Publishing, Ltd.