High velocity clouds (HVCs) are H I clouds that move with large speed (${mid}V_{LSR}{mid}$ >100 km/s) in the halo of the Milky Way. It is now evident that at least some populations of HVCs originated from extragalactic sources, either primordial gas left over from the galaxy formation or gaseous material stripped off from other galaxies closely passing by the Milky Way. HVCs with extragalactic origin play an important role in the star formation of the Milky Way when they eventually collide with the disk of the Milky Way. Although it is still observationally controversial whether HVCs are surrounded by dark matter or not, it is theoretically interesting to investigate the effect of dark matter on the collision of HVCs with the disk of the Milky Way. We model this scenario by using hydrodynamic simulations and search for proper parameters that explain the currently available observations such as the Smith Cloud that is thought to have collided with the Galactic disk already.