In this study, the characteristics of vortex-induced vibration (VIV) of a rigid, smooth circular cylinder elastically mounted in the water flow are investigated. The cylinder has one degree of freedom and is constrained to oscillate only in the vertical direction. The flow Reynolds number lies within the Transition of Shear Layer 3 (TrSL3) region of the subcritical flow regime. The governing equations, namely the continuity and Navier-Stokes equations, are solved using computational fluid dynamics (CFD). The finite volume method is employed for discretizing the equations, implemented through the ANSYS Fluent software. The Pressure Based solver and the PISO algorithm are utilized to couple the equations. The two-dimensional unsteady Reynolds-averaged Navier-Stokes (URANS) equations are solved using the k-ω SST turbulence model. A simplified mathematical model describes the system dynamics and fluid forces associated with the cylinder’s vortex-induced vibration. Examination of the vortices shed in the wake region reveals a P+S vortex shedding pattern. Additionally, the time history of the cylinder’s displacement ratio exhibits a sinusoidal shape, whereas the recorded lift and drag coefficient data are non-sinusoidal due to the P+S vortex shedding mode. Frequency analysis of the cylinder’s response indicates that the oscillation frequency of the cylinder matches the dominant frequency of the lift force. Furthermore, the dominant frequency of the drag force is twice that of the lift one.