We present a method (DMESH) for nonrigid cyclic motion analysis using a series of velocity images covering the cycle acquired, for example, from phase-contrast magnetic resonance imaging. The method is based on fitting a dynamic finite-element mesh model to velocity samples of an extended region, at all time frames. The model offers a flexible tradeoff between accuracy and reproducibility with controllable built-in spatiotemporal smoothing, which is determined by the fineness of the initially defined mesh and the richness of included Fourier harmonics. The method can further provide a prediction of the analysis reproducibility, along with the estimated motion and deformation quantities. Experiments have been conducted to validate the method and to verify the reproducibility prediction. Use of the method for motion analysis using displacement information (e.g., from magnetic resonance tagging) has also been explored.