The SWE are a system of two nonlinear hyperbolic PDEs that must be numerically solved to describe the time evolution of the fluid velocity and water depth in the entire computational domain. Finite-difference methods to obtain approximate numerical solutions are described in this chapter. First, basic numerical aspects are presented. The implementation of boundary conditions for continuous and discontinuous flows is then discussed, and various schemes widely used are explained in detail. The performance of these schemes is assessed using analytical solutions and experimental data for selected test cases.