The Muskingham method uses two formulas to describe the translation of flow surges in a river bed. The continuity formula is the first formula, while the relationship between the reach’s storage, inflow, and outflow is the second formula (the discharge storage formula); these formulas are applied to a portion of the river between two river cross sections. Several methods can be utilized to estimate the model’s parameters. This section contrasts the conventional graphic approach with three numerical methods: Genetic algorithm, Exponential regression, and Classical fourth-order Runge–Kutta. This application’s most noticeable plus point was the need to employ a few hydrological variables, such as intake, output, and duration. The location of the Euphrates entrance to the Iraqi territory in Husaybah city was chosen with its hydrological data during the period (1993–2017) to conduct this study. The goal function is established by accuracy criterion approaches (Sum of squares error and sum of squared deviations). Depending on the simulation findings, the suggested predictive flood routing ideawas highly acceptable with the prospect of adopting the Genetic Expression Programming model as a suitable and more accurate replacement to existing methods such as the Muskingum model and other numerical models, where this method gave results (��2 = 0.9984, SSQ = 1.06, SSSD = 80.75), These results achieved a hydrograph that is largely identical to what was given by the hydrological method called Muskingham.