A classical problem in vortex-induced vibration is to know the flow field past an oscillating cylinder. In this paper we use system theory to identify the oscillatory behaviour of a circular cylinder from flow variables in the wake. We use numerical simulations (CFD) of the flow past a cylinder oscillating in the cross-flow direction at different oscillation frequencies and amplitudes to construct a transfer function that relates the displacement of the cylinder and the resulting flow field. This transfer function can then be inverted to ‘predict’ the displacement of the cylinder given the flow field (as determined by simulations or measurements). We investigate this technique in the so-called lock-in region, where the vortex shedding frequency is synchronised with the oscillation frequency of the cylinder.