We present a parametrized model of the intracluster medium that is suitable for jointly analysing pointed observations of the Sunyaev–Zel'dovich (SZ) effect and X-ray emission in galaxy clusters. The model is based on assumptions of hydrostatic equilibrium, the Navarro, Frenk and White model for the dark matter and a softened power-law profile for the gas entropy. We test this entropy-based model against high and low signal-to-noise ratio ratio mock observations of a relaxed and recently merged cluster from N-body/hydrodynamic simulations, using Bayesian hyperparameters to optimize the relative statistical weighting of the mock SZ and X-ray data. We find that it accurately reproduces both the global values of the cluster temperature, total mass and gas mass fraction (fgas), and the radial dependencies of these quantities outside the core (r > 100 kpc). For reference, we also provide a comparison with results from the single isothermal β model. We confirm previous results that the single isothermal β model can result in significant biases in derived cluster properties.