Genetically-controlled plant resistance can reduce the damage caused by pathogens. However, pathogens have the ability to evolve and overcome such resistance. This often occurs quickly after resistance is deployed, resulting in significant crop losses and a continuing need to develop new resistant cultivars. To tackle this issue, several strategies have been proposed to constrain the evolution of pathogen populations and thus increase genetic resistance durability. These strategies mainly rely on varying different combinations of resistance sources across time (crop rotations) and space. The spatial scale of deployment can vary from multiple resistance sources occurring in a single cultivar (pyramiding), in different cultivars within the same field (cultivar mixtures) or in different fields (mosaics). However, experimental comparison of the efficiency (i.e. ability to reduce disease impact) and durability (i.e. ability to limit pathogen evolution and delay resistance breakdown) of landscape-scale deployment strategies presents major logistical challenges. Therefore, we developed a spatially explicit stochastic model able to assess the epidemiological and evolutionary outcomes of the four major deployment options described above, including both qualitative resistance (i.e. major genes) and quantitative resistance traits against several components of pathogen aggressiveness: infection rate, latent period duration, propagule production rate, and infectious period duration. This model, implemented in the R package landsepi, provides a new and useful tool to assess the performance of a wide range of deployment options, and helps investigate the effect of landscape, epidemiological and evolutionary parameters. This article describes the model and its parameterisation for rust diseases of cereal crops, caused by fungi of the genus Puccinia. To illustrate the model, we use it to assess the epidemiological and evolutionary potential of the combination of a major gene and different traits of quantitative resistance. The comparison of the four major deployment strategies described above will be the objective of future studies.