The Lena River is one of the largest rivers in the Arctic and has the largest delta. Given the large territory of the Lena Delta, the direct measurements are by far insufficient, calling for a modeling approach. However, most of the models, which include the Laptev Sea shelf zone, do not resolve the Lena Delta and as a consequence lose information about Lena river stream changes using input data with insufficient quality. In the current work we present the hydrodynamics model for the Lena Delta region and full baroclinic model for the Laptev Sea shelf area. The available hydrological information in the Lena Delta was collected, analyzed and used for the model verification. The developed hydrodynamics model provides the first necessary step for the further modeling efforts in the area. It also gives an input for the larger scale models resolving hydrodynamics of more than twenty main Lena River freshwater channels with switched on wetting/drying option. Additionally the Lena Plume dynamics in the Lena Delta region of the Laptev Sea are explored by us in simulations performed with the FVCOM (Finite Volume Coastal Ocean Model). The impact of winds and tides on the Lena plume propagation is an alysed based on simulations for the summer season of 2008 and also on idealized experiments. For that period, the simulated distributions of temperature and salinity agree well with the observations,including the thickness and border position of the buoyant plume. The model simulates the most energetic semidiurnal and diurnal tidal constituents. The amplitudes and phases of the tidal components at the open boundary were derived from AOTIM5 and TPXO7.1 with corrections. These corrections noticeably improve the agreement of the modelled tidal maps with available tide gauge data.