Two widely used channel routing models are the Muskingum and Muskingum-Cunge (M-C) models. However, no significant research has been conducted on how input parameter uncertainty and model sensitivity affect the accuracy of the downstream hydrograph. Therefore, the goal of this research was to perform uncertainty and sensitivity analyses of the Muskingum and M-C models. The results of the sensitivity analyses show that neither model is particularly sensitive to variations in channel routing input parameters, although the Muskingum method is slightly more sensitive. The results of the uncertainty analyses indicate that in all models uncertainty in the channel routing input parameters introduce only a moderate amount of error in the downstream hydrograph; whereas uncertainty in the upstream hydrograph could introduce significant errors. Finally, the M-C method gave negative outflows in the first few time steps, in agreement with other widely reported results in the literature; however, while others have claimed that negative outflows do not have a significant effect on the downstream hydrograph, the results presented herein suggest that this is not always true.