A series of numerical simulations were performed to investigate the influences of storage vessels shapes on sloshing dynamics under horizontal excitation by employing the open source code OpenFOAM, which has been extensively validated by experimental data for the sloshing flow problem. The results show that the membrane liquefied natural gas (LNG) tanks are subject to lower impact pressure than the cylindrical, rectangular and spherical tanks with the same volume of liquid and the overall tank dimensions, as the slope at the storage vessels bottom changes the flow direction of the liquid and therefore reduces the impact on the vertical wall. In the cylindrical and spherical tanks, higher impact pressure was found on the wall directly opposite to the excitation direction and the maximum impact point will shift away from the external excitation direction as the wave breaks up violently until a quasi-steady state of the sloshing wave rotating along the side wall is reached. The curved surface of the spherical tank could also help reduce the impact pressure when compared with the cylindrical tank.