Under water cavitation occurs when the liquid changes the phase into its vapor due to the local pressure is lower than the water saturation pressure. If a body is moving very fast under water, the local pressure around it at a certain flow regime will be lower than the water saturation pressure. The cavitation around the body will occur. Following the increase of the intensity of the cavitation, a cloud cavitation will occur. Under the cloud cavitation occurrence, the cavitation is unsteady and periodic, which involves formation, detachment and collapse of sheet cavities. In this paper, large Eddy simulation (LES) is employed together with a mixture assumption and a finite rate mass transfer modeling into OpenFOAM to study the cavitation phenomena. The validation comparisons of numerical simulations with experiments of a sphere under water are performed. After the validation, a full submarine model with sail and appendages under water is studied. The submarine is under water around 450 m deep with a moving speed at 60 m/s. It is found that the cavitation changes under the different cavitation numbers (from 1.0 to 0.1). Small cavitation numbers induce a large area cavitation, whereas large ones reduce this phenomenon. A supercavitation, which can be described as a large bubble, is found around the high speed submarine at cavitation number equals to 0.1.