Regulation of fluid flow by deformations of the surrounding elastic structure is observed in many natural and artificial system, such as in the cardiovascular system. As the first step to study the regulation of oscillating flows, we consider synchronization of vortex shedding past a cylinder within an elastic structure with a sinusoidal external forcing. We use phase-reduction theory to evaluate the synchronization characteristics of the oscillating fluid–structure coupled dynamics. We find that the phase-sensitivity function, which characterizes the phase-response of the oscillation, is significantly affected by the Cauchy number and slightly affected by the fluid-to-structure density ratio and Poisson's ratio of the structure material, for fixed model configuration and Reynolds number. The predicted synchronization characteristics are in close agreement with results from direct numerical simulations. The synchronization region is maximized when the sinusoidal perturbation is applied near the downstream end of the cylinder. These findings open further possibility for the utilization of phase-reduction theory to characterize synchronization in other practical problems exhibiting fluid–structure coupled dynamics, such as in biological systems and the control of microfluidics.