The size-dependence of the linear depolarisation ratio of mineral dust aerosols is investigated. Laboratory measurements on 131 different aerosol samples with varying size distributions and mineralogical compositions are fitted with a homogeneous spheroid model. A minimum-bias and minimum-variance fit of the data is obtained for prolate model particles with a refractive index of 1.525+0.001i and an aspect ratio of 0.87. The model error is analysed by varying the input parameters to the light-scattering computations. It is found that the scattering of the measurements about the model can mainly be explained by variation of the morphology and dielectric properties, and to a much lesser extent by variation in the geometric standard deviation of the size distribution. The modelling of the data is extended by using size-shape distributions of spheroids. The results indicate that there is some freedom in choosing the best-fit weights of the shape-distribution of spheroids, which could potentially be useful when extending the model to multiple wavelengths, or to including additional optical parameters other than depolarisation. However, it is also found that the most reasonable fits of the data are obtained by mildly aspherical prolate and oblate spheroids, which limits the freedom of adjusting the best-fit weights.