The numerical model DynaRICE and its application to ice jam formation and release is presented. The model is a two-dimensional coupled flow and ice dynamic model. The ice dynamic component, which includes both the internal ice resistance and boundary friction on ice motion, uses a Lagrangian SPH method. The hydrodynamic component of the model uses a streamline upwind finite element method, which is capable of simulating trans-critical flow conditions. The model is validated with field observed ice jam data. The phenomena of ice jam formation and release dynamics are examined using the validated model.