Abstract: During the past several decades, researches on physical features of vortex rings have not been well understood. Shariff (Annu.Rev.Fluid Mech. 1992, 24: 235-79) summarized the researches on the evolution and transmission process of vortex rings, Dabiri (Annu.Rev.Fluid Mech. 2009, 41: 17-33) further explores the dynamic feathers of vortex ring and the effect on bio-propulsion system, the aim of researches on vortex ring is to reveal the fundamental reasons why animals can product high lift force and large thrust. However, the formation and evolution of vortex ring and the corresponding fluid dynamics both lack thorough analysis. One important reason is that the boundary and physical feather parameters cannot be determined clearly. In this paper, the evolution process of vortex rings is solved by numerical simulation, and then the boundary of vortex ring is defined on the basis of stream function with body coordinate system, meanwhile, the physical feathers of vortex ring with different formation times(the stroke of piston/the diameter of piston) can be investigated. Compared with the Gharib′s(J.Fluid Mech. 1998, 360:121-140) experimental conclusions and the analytical results based on Slug model, stream function method can determine the boundary of vortex ring and the physical parameters of vortex ring reasonably. Moreover, the vortex core radius increases with formation time, but the ability of entrainment decreases with formation time, when the formation time of vortex ring is smaller than four. However, when the formation time exceeds four, the radius of vortex ring core no longer increases with formation time and the entrainment ability begins to increase.