Abstract: In this paper we propose a new numerical scheme to simulate the river flow in the presence of a variable bottom surface. We use the finite volume methods, our approach is based on the technique described by D. L. George for shallow water equations. The main goal is to construct the scheme, which is well balanced, i.e. maintains not only some special steady states but all steady states which can occur. Furthermore this should preserve non–negativity of some quantities, which are essentially non–negative from their physical fundamental, for example cross section or depth. Our scheme can be extended to the second order accuracy. We also describe connections between the central and central-upwind schemes and the approximate Riemann solvers.