Proper orthogonal decomposition (POD) or dynamic mode decomposition (DMD) are useful analytical techniques for describing the behavior of a complicated flow by decomposing the flow into several components called modes. In POD analysis, the flow is most efficiently decomposed into orthonormal modes in terms of energy, so most of the flow energy can be extracted using a small number of modes. On the other hand, in DMD analysis, flow structures that have specific frequencies can be observed by managing the sequence of the given time series data. In this study, POD and DMD analyses were applied to the experimental and numerical results for velocity fields around a circular cylinder, and the analytical results were compared. As a result, flow structures of POD and DMD modes from the experimental results were mostly in agreement with those from the numerical results, but differences were seen in energy distribution. In the POD analysis, the rates of energy in the numerical results were clearly divided in each pair of POD modes, but in the experimental results, they were not clear except for the first and second POD modes.