A mathematical model of the process of pollution of the aquatic environment with oil products at the rupture of an oil pipeline crossing a river bed is presented. To describe this process, Reynolds equations are used for turbulent flow. The discrete analogue is obtained using the finite volume method. As a result of the numerical solution, the influence of the river parameters and the characteristics of the source of pollution on the process of distribution of petroleum products in the aquatic environment were studied. The results of mathematical modelling of oil spills can be used in the development of preventive measures to detect and prevent the spread of pollution.