The aim of this computational study is the investigation of the effects of the transverse oscillations of a cylinder on the flow pattern and on the hydrodynamic forces exerted on the body. The finite element technique was used for the solution, which comprised numerical flow visualization and evaluation of the hydrodynamic forces, at a constant Reynolds number equal to 106. The cylinder oscillation frequency was varying between 0.8 and 1.2 of the natural shedding frequency, and the oscillation amplitude was equal to 40% of the cylinder diameter. For values of the cylinder oscillation frequency lower or equal than the natural shedding frequency the vortex pattern is similar to that observed for a fixed cylinder, whereas for higher, a more complicated aperiodic pattern is obtained. The effects of the frequency of the cylinder oscillation on the lift force, the phase angle between the lift and the cylinder displacement and on the timing of vortex shedding are also discussed.