The river routing methods used for flood forecasting mainly rely on hydrological and simplified hydraulic methods. Due to differences in difference schemes and simplified forms of dynamic equations, there are certain differences in the simulation accuracy and numerical stability among these routing methods. Further study are needed through numerical experiments to select suitable confluence methods for river routing in practical applications. Although existing simplified hydraulic methods have been widely applied in many hydrological models, their applicability and simulation accuracy still need further exploration and research. This study compares four simplified hydraulic methods, Muskingum-Cunge-Todini (MCT), nonlinear reservoir, first-order explicit diffusion wave, and local inertial wave, with MIKE11 dynamic wave simulation results through a series of ideal river channel experiments, and the accuracy and the numerical stability of these four routing methods were analyzed under different riverbed slopes and river widths. The results indicate that nonlinear reservoir routing, MCT, diffusion wave, and local inertial wave methods are more suitable for rivers with the channel bed slope greater than , while the river width has little impact on the above three methods. Nonlinear reservoir method does not suffer from computational instability, and the stability of the other three methods decreases in the following order: MCT, local inertial wave, and diffusion wave. The first-order explicit diffusion wave method used in this study has low simulation accuracy and is highly unstable. In future research, higher order and more stable diffusion wave formats can be sought to replace this method. This study can determine the applicable condition, simulation accuracy, and stability of these river routing methods, providing reference for the practical application of the above routing methods for different rivers.