A two part probabilistic model for polycrystalline microstructures is described. The model utilizes a Poisson–Voronoi tessellation for the grain geometry and a vector random field model for the crystallographic orientation. The grain geometry model is calibrated to experimental data through the intensity of the Poisson point field underlying the Poisson–Voronoi tessellation and the orientation random field is calibrated to experimental data through its marginal distributions and second moment properties. Realizations of the random microstructure are generated by use of translation methods and are used, with simplified mechanical models, to investigate the problem of intergranular fracture. It is found that intergranular cracks exhibit some statistical properties of a scaled Brownian motion process.