Refrigeration by an active magnetic regenerative system (AMR) is potentially more attractive, as compared to conventional techniques. Indeed, devices based upon an AMR cycle are more efficient, compact, environment-friendly and can operate over a broad range of temperatures. In this paper, attention is focused to the near room-temperature range. On the other hand, however, the AMR cycle poses a variety of complex problems, in terms of fluid dynamics, heat transfer and magnetic field. In order to identify the optimal operational parameters, the design and optimization of a magnetic refrigeration system can be supported by modelling. In this paper, a dimensionless approach was adopted to simulate an AMR cycle following a Brayton regenerative cycle. In the simulation, the temperature range that has been explored is 260 - 280 K and 275 - 295 K. The heat transfer mediums are, respectively, water-glycol mixture (50% by weight) and pure water. The Gd0.8Dy0.2 alloy and pure Gd have been chosen as constituent material for the regenerator of the AMR cycle. With this model, the influence of the different parameters on cycle efficiency has been analysed. In particular, the study has been focused on the influence of the secondary fluid properties, magnetic material particle diameter, fluid blow time, secondary fluid mass flow rate, regenerator geometry and effect of axial thermal conduction. The model enables to find optimal dimensionless numbers in order to maximize the cycle performances. The results can be extended to widely different situations and therefore can be easily employed for the design and the optimization of new experimental prototypes. Copyright (c) 2012 John Wiley & Sons, Ltd.