This study investigates the dynamics of waves generated by landslides in narrow bays with parabolic cross-sections. The wave phenomena in narrow bays is a two-dimensional problem. However, for relatively narrow and long bays, the flow component across the cross-sectional area can be assumed to be uniform, and the original two-dimensional model can be reduced to quasi one-dimensional Saint-Venant equation. A numerical study was conducted to understand wave evolution in inclined bottom. The previously developed numerical scheme, called momentum conserving staggered grid (MCS), was modified to accommodate landslide movements. The numerical simulation results are then validated against analytical solutions. The findings indicate that the numerical and analytical solutions are in good agreement, suggesting that the MCS scheme effectively describes wave dynamics in narrow bays with parabolic cross-sections.