Floods have consistently been one of the most significant natural disasters affecting humans. In a country like Iran, their impact is particularly pronounced due to the irregular patterns of rainfall both in space and time. Flood routing is a crucial aspect of hydraulic engineering, as it enables the prediction of how floods will rise and recede at specific points along a river. Various techniques and methods are employed to address routing problems. This Manuscript explores routing using Muskingum's method, the least squares error method, and neural networks. First, three proposed neural network models with different transfer functions were evaluated to identify the best-performing model. The results were then compared using the least squares method and validated against the model proposed by Choudhury and Sankarasubramanian (2009). Ultimately, both models yielded acceptable results; however, considering the RMSE values, the least squares error method's results are closer to those proposed by Choudhury and Sankarasubramanian (2009).