Abstarct: In this thesis, the Roe finite volume method is used to solve the two dimensional depth averaged shallow water equations. First, the extraction of the equations from three-dimensional Navier-Stokes equations is expressed. Then these equations are discreted using Roe finite volume scheme. Next, a computer code is written for solving these equations and for getting assured of the proper operation of the numerical model. Two numerical examples are performed and compared with analytical results. Finally flow in T-junction on open channels is simulated numerically; the results are compared with other researcher’s numerical and experimental results. The effect of different roughness on vortex length in branch channel and flow distribution in channels baxsed on inflow Froude number is also considered.