||Steady incompressible flow past an infinitely long circular cylinder has been a classical problem of fluid mechanics for more than a century. As the cylinder diameter D and the viscous diffusion distance δD(= √(vD / U∞) which is the maximum boundary layer thickness) are the only two length scales involved, the problem is governed by one parameter, the length scale ratio, i.e., Reynolds number ReD = (D/δD)2 = U∞D/v, where U∞) is the flow velocity at far away and v the kinematic viscosity of fluid. However, the cylinder is always of finite length in practice. In experiments, flat plates are usually attached to the cylinder ends to prohibit the disturbance of crossflows. As a result, two new geometric parameters are added to this problem. They are the cylinder length aspect ratio H/R and endplate aspect ratio Ro/R, where H is the half cylinder length, Ro the endplate radius and R (= D/2) the cylinder radius. In the present study, 3D numerical simulations on flows past a circular cylinder of infinite length and of finite length with endplates were performed. For infinitely long cylinder (H/R → ∞), periodic boundary condition was used for the spanwise direction when a finite computation domain is adopted. The simulation results have basically recaptured the 2D flow behaviors at low Reynolds number such as formation of vortex bubble behind the cylinder and the 2D vortex shedding, and those at moderate Reynolds number such as 3D vortex shedding. These 3D simulations of flows past an infinitely long cylinder provide not only a rigorous validation of the code, but also serve as the database for comparison of the later results of finite H/R. For the finite cylinder with endplates, the 3D simulations were performed by varying Reynolds number and cylinder aspect ratio, with the endplate aspect ratio fixed at Ro/R = 50. Due to the requirement of long computation time for turbulent wake at high Reynolds number, only laminar flows at low and intermediate ReD , with H/R ranging from 0.005 to 50 from Hele-Shaw flows to flows with vortex shedding, were reported in this thesis (Results of turbulent wake for high ReD will be reported in a subsequent report). Even though, a wide variety of 3D flow phenomena are encountered. These include the 3D patterns of Hele-Shaw flow, helical motion in the steady vortex bubbles, and beating phenomenon and vortex dislocations during vortex shedding. Furthermore, the associated forces, i.e., the drag and lift forces on the cylinder and the shear stress distribution on the endplate, are also discussed.