Flows and contaminant transport in the Novosibirsk reservoir are calculated on the basis of a two-dimensional (plane) nonstationary model with Saint Venant's equations. The model allows for the presence of a large number of islands. Coefficients of horizontal exchange (dispersion) are calculated by the formula taking into account dynamic velocity at the bottom. Numerical implementation of the model employs a semi-implicit conservative finite-difference TVD scheme on a distributed grid and procedures allowing for the flow past these islands. Model examples of calculations and computation results for dynamics of long-range transport of contaminants along the Novosibirsk reservoir are given.