Abstract It is important to understand how water waves propagate through water channels in order to reduce inundation damages induced by surges and/or tsunami run-up. For this purpose, a two-dimensional numerical model is developed based on Nonlinear Shallow Water Equations. In order to appropriately describe the strongly nonlinear hydrodynamics, a high-order TVD scheme is implemented. Model capabilities are confirmed through comparison with existing analytical studies including the dam-break problems, run-up and back-wash on a sloping bathymetry. The model is then applied to the study on the inundation of bore propagating in a channel of parabolic cross-section from a side breach.