Recently, the awareness regarding environmental issues is increasing all over the world. Natural gas is a good energy option because of its environmental performance. This leads to the usage of liquefied natural gas (LNG) as an attractive fuel alternative for shipping. Regarding the transportation of LNG, Moss type tank, a spherical tank, is one of the popular cargo containment systems due to its excellent structural integrity. In order to increase the volume capacity of the spherical tank, a stretched tank which is a hybrid of partial spheroids and a vertical cylinder has been developed. As for the fuel gas tanks, capsule-shaped tanks are commonly used. The capsule-shaped tank usually consists of a horizontal cylinder and two half spheroids at its ends. There are a variety of shapes and sizes in the capsule-shaped tanks depending on their intended uses, also they can be reinforced by bulkhead structures if necessary. The common point for Moss type tanks and capsule-shaped tanks is that they may be used as partially filled tanks because of their possible advantage in sloshing compared to prismatic tanks. Sloshing has been an issue of concern in shipping partially loaded liquified natural gas. In this research, behaviors of the partially filled stretched tanks of LNG carriers and capsule-shaped tanks of gas fueled vessels are examined. Almost two-dimensional free surface motion in the tank, i.e., sloshing, and three-dimensional rotating motion of the free surface, i.e., swirling, were typical free surface motions observed. Swirling easily occurs in the stretched tanks. In the capsule-shaped tanks, we observed multiple swirling, i.e., two or more rotating motions of free surface are generated inside the tanks, when they are excited in their transverse direction. The force and the pressure on the tank wall were also studied by both model experiments and numerical simulations. With respect to the force on the capsule-shaped tank's wall, the magnitude of the force is not significant if the tank is excited in the longitudinal direction of the tank. It should be noted, however, that the natural frequency of the free surface motion in the tank can be close to the ship motion's natural frequency when it is excited in the tank's longitudinal direction.