The problems of mathematical modeling of hydrodynamics of open flows are analyzed in the article when general sizes of bridge crossings with group holes are assigned. Most of the existing methods for calculating branched flows are based on the use of one-dimensional models, it does not allow to describe sufficiently the hydrodynamic processes occurring in zones with separated flows. Therefore, in the calculation of bridge crossings with group holes, two-dimensional models that take into account the features of the morphology of natural watercourses, the uneven distribution of the average velocities along the vertical, the phenomenon of flow separation, as well as the change in rate along the flow due to the separation of the flow is suggested. The existing experimental and theoretical studies are analyzed, the flow structure and the physical model of the flow branching process in the zone of influence of bridge crossings with group holes are considered. Based on the fundamental equations of flow transfer, a mathematical two-dimensional model of the flow of open flows is presented, which takes into account the influence of secondary currents. To substantiate the zone of influence of bridge crossings with group holes, an equation for vorticity is proposed that reflects the distribution of vortex structures. For the closure of the equations of motion and continuity, algebraic relations for the Reynolds stresses in conjunction with the two-parameter k-ε model for depth-averaged values are used, which is modified to take into account the effect of the curvature of the flow. The method of numerical realization of the proposed mathematical model is based on the predictor-corrector method using the McCormack scheme, modified by splitting the model equations with respect to spatial coordinates and time. The method of successive upper relaxation based on the Gauss-Seidel iterative method is used to realize the algebraic relations of turbulent stress transfer. The conclusion is made about the expediency of practical application of this model