The numerical simulation of the flow past a circular cylinder forced to oscillate transversely to the incident stream is presented here for a fixed Reynolds number equal to 100. The 2D Navier-Stokes equations are solved with a classical Finite Volume Method with an industrial CFD code which has been coupled with a user subroutine to obtain an explicit staggered procedure providing the cylinder displacement. A preliminary work is conducted in order to check the computation of the wake characteristics for Reynolds numbers smaller than 150. The Strouhal frequency fS, the lift and drag coefficients CL and CD are thus controlled among other parameters. The simulations are then performed with forced oscillations f0 for different frequency rations F = f0/fS in [0.50–1.50] and an amplitude A varying between 0.25 and 1.25. The wake characteristics are analysed using the time series of the fluctuating aerodynamic coefficients and their FFT. The frequency content is then linked to the shape of the phase portrait and to the vortex shedding mode. By choosing interesting couples (A,F), different vortex shedding modes have been observed, which are similar to those of the Williamson-Roshko map.