This dataset gathers theoretical analysis and experimental results on a number of anisotropic materials. Materials considered are sapphire, exhibiting uniaxial linear birefringence, topaz, exhibiting biaxial linear birefringence, and crystalline quartz, exhibiting both uniaxial linear birefringence and optical activity. The data relate to a set of experiments aimed at verifying a novel generalised analytical method for describing the effect of anysotropic materials on polarised light propagating at arbitrary angles with respect to the optic axes of the material.