A new process-based approach is introduced for a more efficient computation of the overflow-induced growth of an erosional channel in a noncohesive homogeneous narrow landmass such as the breach growth in a sand-dike. The approach is easy to incorporate in a 1D/2DV morphodynamic model to compute the channel growth both vertically and laterally. The flow modeling is based on the shallow water equations. For modeling the channel growth, a set of closed equations describing the channel growth in both vertical and lateral direction has been derived in connection with several new morphologic parameters such as the representative channel width and the channel cross-sectional growth index. The approach has been applied to simulate the breach growth in sand-dikes and the morphological development of wave overwash across sand barriers. The computational results bear fairly good resemblance with existing experimental data.