Vortex induced vibration of a circular cylinder in an inclined flow is a major subject in this thesis, the interaction and effect between a moving cylinder and fluid is always focused and investigated. We used a finite differences method to get the forces on cylinder, and then combined a Runge-Kutta four order approximate method to get a new position of a cylinder at next time step, repeated above procedure and we will get the solutions of a time series of cylinder response for VIV simulations. Most of papers focus on the peak amplitude and its scale due to the shedding frequency of system is near or at the fs, where fs is the shedding frequency of a uniform flow past a stationary cylinder. Except the ¡§first resonance¡¨, we found the ¡§second resonance¡¨ in the VIV simulations. The ¡§second resonance¡¨ occurs due to the natural shedding frequency of system is near or at the twice of the reduced frequency of the oscillator ¡§fs=2F1¡¨. The natural shedding frequency of a body is a key parameter, it always be discussed its effect and importance, and its value is also presented the frequency of lift force (or displacement on Y direction) of a body. On the contrary, the frequency of in-line force (or displacement on X direction) and its effect is seldom be investigated and discussed. In this study, we will discuss the effect of frequency of in-line force and the scale of ¡§first resonance¡¨ and ¡§second resonance¡¨ for VIV simulations. In order to verify the accuracy of our numerical model, this study simulated four different types for the cases of uniform flow past a circular cylinder with stationary, streamwise, transversal and rotational oscillating, respectively. The simulation results are compared with the study results of other paper by experimental and numerical methods, and the comparison show good agreement and high accuracy in the range of the in-line and lift forces on the cylinder, the main wake size behind the cylinder, the vortex shedding mode and the streamline pattern of the flow field. Furthermore, this study investigates a uniform flow past an inclined oscillating cylinder which is forcing oscillation in a range of 00 ~ 900 for the inclined angle (with respect to the X-direction of the Cartesian coordinates system). The effects of giving the different forced frequencies of a cylinder were investigated and discussed. And the application and restriction of Morison¡¦s equation will also be studied and investigated in different input conditions.