In this paper a numerical model is presented for the description of the erosion and sedimentation near pipelines on the sea bottom. The model is based on the Navier-Stokes equations and the equation of motion and continuity of sediment. The results of the simulations have been compared with the results of tests in a large-scale facility. The agreement between the results of the simulations and the experimental results is good. The applicability of the method is twofold: firstly, the processes of erosion and sedimentation around bodies on the sea bottom can be simulated; secondly, the method can be used for the design of pipelines, including erosion stimulating elements, such as spoilers.