Magnetic refrigeration employing the magnetocaloric effect of ferromagnetic materials has been identified as potentially more efficient and cost-effective than conventional refrigeration systems. One magnetic cycle that shows promise for efficiently achieving cooling over large temperature spans is active magnetic regenerative refrigeration (AMRR). In this cycle the magnetic material serves the dual functions of work input and thermal regeneration. The operation of an AMRR is complex, having coupled thermal and magnetic phenomena. This complexity means that a detailed numerical model is required for optimized design purposes. This thesis describes a numerical modelling approach and a solution of the complete 2-dimensional, quasi-steady-state energy equations describing the operation of rotary active magnetic regenerative refrigerators. Effects of solid-fluid heat transfer, conduction in the solid and fluid, fluid entrainment in the solid, electrical eddy current generation, and material magnetocaloric effects are included in the model. Three different solution algorithms are described and the relative benefits and drawbacks of each are compared. One algorithm is selected as the best candidate for future modelling exploration. Selected AMRR results are presented and compared with model results for a rotary passive regenerator.