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Proper orthogonal decomposition (POD) is often employed in developing reduced-order models (ROM) in fluid flows for design, control, and optimization. Contrary to the usual practice where velocity field is the focus, we apply the POD analysis on the pressure field data obtained from numerical simulations of the flow past stationary and oscillating cylinders. Since pressure mainly contributes to the hydrodynamic forces acting on the structure, we compute the pressure POD modes on the cylinder surface oscillating in lock-in and lock-out regions. These modes are then dissected into sine and cosine magnitudes to estimate their contribution in the development of pressure lift and drag decomposition coefficients, respectively. The key finding of this study is that more POD modes are required to capture the flow physics in nonsynchronous regimes as compared to synchronization case. Engineering application of this study is the development of reduced-order models for effective control techniques. [ABSTRACT FROM AUTHOR]