This paper describes a new model of the hydrodynamic system consisting of the Lena River delta and the Laptev Sea shelf zone. The description of a complex fluvial system with many channels, watercourses and estuarine areas is based on the numerical solution of the Saint—Venant equations. The method used is based on the one-dimensional mathematical description of the processes for each segment of the river net and formulation of the coupling conditions for flows at branch points. A scheme adopted here for the interaction with the surrounding areas of the sea shelf implies the unilateral influence of the delta water on the sea currents, i.e., the river is the primary component in the considered system. Preliminary numerical experiments are presented and their results are discussed. With the help of tuning of the model parameters and considering additional physical mechanisms, some possible causes of discrepancies between the results of numerical experiments and observations were identified. The ways of the further improvement of the system of models were outlined and possible problems, that can be efficiently solved, are discussed.