In particulate geomechanics it is common to quantify fabric anisotropy using contact and particle orientations. Measurement of void anisotropy is less common, most likely owing to the difficulties associated with defining individual voids. Here a Delaunay tessellation-based approach is applied to measure anisotropy of the inter-void constriction orientations. This new measure of fabric anisotropy was capable of identifying stress-induced anisotropy in discrete-element modelling true triaxial simulations with spherical particles. A relationship is established between the constriction orientations, the macro-scale principal stress directions and the micro-scale contact normal orientations.