First-order phase transition magnetocaloric materials in multi-stage regenerators are attractive for magnetocaloric refrigeration because of their relatively high available power and the potential for the use of low-cost elements such as iron in their production. In this work a model is used to represent the thermodynamic properties of magnetocaloric materials allowing the magnetocaloric materials to be fully parameterized for the first time. A numerical model is used to carry out a large study including the material parameters and the parameters that describe magnetocaloric machines and their operation. A unique method of evaluating material refrigeration capacity is introduced and used to normalize material inputs.The results are analyzed both in terms of the direct impact of the material parameters and the interactions between machine and material parameters on performance. It was found that machine cooling power was maximized for the cases with the largest adiabatic temperature changes. It was also found that many machine parameters and material parameters interact when determining the performance of a machine. This suggests that materials and machine research would benefit from a closer collaboration. (C) 2016 Elsevier Ltd and IIR. All rights reserved.