The application of numerical modeling of free surface flows to water resources management, environmental and ecosystem protection can be applied for different applications: simulation of flows due to dam failure, simulation of the process of river bed change, simulation of flows and sediment transport, simulation of the evolution of a flood due to high intensity rainfall, etc. In this study, two explicit finite difference numerical schemes with two-stage fractional step and modified two-stage fractional step are used to simulate the dam failure wave. The validation of the results obtained is done against experimental measurements and existing numerical results in the literature specialized in this field of research. These simulation results obtained with the new formulation of the modified two-stage fractional step numerical scheme showed a good fit with the simulated, experimental results and the numerical results of other researchers.