IBM (Immersed Boundary Method) with feedback momentum forcing was applied to stationary and moving bodies. The capability of IBM to treat the obstacle surfaces, especially with moving effect has been tested for two dimensional problems. Stationary and oscillating cylinders were simulated by using IBM based on finite volume method with Cartesian coordinates. For oscillating cylinder, lateral and vertical motions are considered, respectively. Present results such as time histories of drag and lift coefficients for both stationary and oscillating cases are in good agreement with previous numerical and experimental results. Also, the instantaneous wake patterns of oscillating cylinder with different oscillating frequency ratios well represented those of previous researches. More feasibility study for IBM has been carried out to two oscillating cylinders. Drag and lift coefficients are presented for two cylinders oscillating sinusoidally with phase difference of $180^{circ}$.