The quantum mechanics model of a magnetic Stirling cooler is established. The optimal relation between the cooling load and the coefficient of performance (COP) is obtained. The maximum cooling load and corresponding COP as well as the maximum COP and the corresponding cooling load are derived. The optimization criteria for a magnetic Stirling cooler are determined. The results obtained here will be useful for the further understanding and the selection of the optimal operating conditions for a magnetic Stirling cooler. Published in 2002 by John Wiley Sons, Ltd.