Variable reluctance permanent magnet machines exhibit shear stresses higher than conventional machine topologies. However, analysis and design of these machine topologies is not straightforward owing to the nature of the flux paths in the machine. In a transverse flux machine flux flows in all three dimensions and the machine structure is non-conventional. The vernier hybrid machine is another member of this family, but the flux paths are restricted to two dimensions, and can therefore be constructed using laminations. Significant leakage flux paths exist in the vernier hybrid machine, which must be modelled accurately during machine design. The use of flux-linkage maps to determine the performance of a linear vernier hybrid machine is described. Experimental results are presented to verify the model. The technique can be applied to any variable reluctance permanent magnet machine topology.