<p>Odd elasticity introduces active moduli to the antisymmetric components of the elastic tensor, which describe the asymmetric coupling between different deformation modes in a medium and quantify the work extracted during quasi-static strain cycles. The introduction of active moduli renders the elastic tensor non-Hermitian, breaking the Maxwell-Betti reciprocity and enabling the observation of phenomena that cannot occur in traditional passive media. Here, we develop an analytical dynamic model for odd elastic circular plates to investigate the effects of odd elasticity on motion in rotationally symmetric geometries. We report a novel nonreciprocal rotating wave and explore the effects of different odd elastic moduli on chiral deformation. Nonreciprocal rotating waves represent a distinct dynamic mode, exhibiting unidirectional propagation with amplitude increasing or decreasing exclusively along a specific direction. The amplitude change during motion reveals the system’s non-conservation of energy.</p>