Tailings formed during the mining and beneficiation of iron ore are sources of intensive dust generation. In order to assess the intensity of dust formation and determine the effectiveness of methods of its reduction, it is necessary to know the local velocity of the air flow near the various surfaces of the tailings storage facility. For the theoretical solution of this problem, a CFD model was developed, which allows determining the velocity field of the air flow when flowing around the tailings storage facility. The model allows you to obtain the value of the wind speed near the surfaces of the structure and, based on this information, to make a forecast of possible dust formation. The constructed CFD model is based on the use of an aerodynamic model of potential motion. The modeling equation is the Laplace equation for the velocity potential. To build a numerical model, the idea of establishing a solution in time is used, therefore numerical integration of the “unsteady equation” for the velocity potential is carried out. Numerical integration is carried out using the finite-difference method of total approximation. The results of the computational experiment are presented.