This paper reports simulation results for free-stream flow past an oscillating square cylinder at Re=100 and 150, for oscillating-to-natural-shedding frequency ratios of 0.5≤fr≤3.0 at a fixed oscillation amplitude of 0.2 of the cylinder width. The transformed governing equations are solved in a non-inertial frame of reference using the finite volume technique. The 'lock-in' phenomena, where the vortex shedding becomes one with the oscillation frequency, is observed near the natural shedding frequency (fr≈1). Beyond the synchronization band, downstream recovery of the wake to its stationary (natural) state (frequency) is observed in cross-stream velocity spectra. At higher forcing frequencies, a phase lag between the immediate and the far wake results in a shear layer having multi-polar vortices. A 'Vortex-switch' accompanied by a change in the direction of energy transfer is identified at the 'lock-in' boundaries. The variation of aerodynamic forces is noticed to be different in the lock-in regime. The velocity phase portrait in the far wake revealed a chaotic state of flow at higher excitation though a single (natural) frequency appears in the spectra. Copyright © 2008 John Wiley & Sons, Ltd.