A nonlinear model of a warm-core ring is presented here. The model treats the warm-core ring as a confined lens of fluid rotating on an f plane. A simple polynomial expansion of the hydrodynamic field variables about the center of mass of the lens provides the basis for an exact reduction of the hydrodynamic equations. Observations from two warm-core rings are compared with simulations from the nonlinear model. Fair agreement is found between model calculations and observations from the Gulf Stream and the Kuroshio.