Rotating crop cultivars with different resistance genes could slow the evolution of virulent strains of fungal pathogens, but could also produce highly virulent pathogen strains. We present a new model that links polycyclic pathogen epidemiology and population genetics in order to predict how different strategies of rotating cultivars with different resistances will affect the evolution of pathogen virulence and the breakdown of crop resistance. We modelled a situation where there were four different resistance genes that can be deployed within each crop cultivar, and four virulence genes that may be present within the pathogen. We simulated four different rotational management strategies: (i) no rotation; (ii) a different gene every year; (iii) a different gene every 5 years; and (iv) a different combination of two stacked genes each year. Results indicate that rotating cultivars can lead to longer periods of disease suppression but also to the selection of highly virulent strains. The efficacy and relative advantage of different resistant cultivar rotation strategies depended on the fitness penalties, initial virulence allele frequencies, and ability of non-virulent pathogen genotypes to grow and reproduce on resistant cultivars. By capturing the essential processes involved, our model provides a useful new tool for investigating the evolutionary dynamics of pathogen virulence and crop resistance breakdown.