White dwarfs provide a unique opportunity to probe exoplanetary material and showcase the rich dynamics of post-main-sequence planetary systems. Increasing observations of metallic pollution and disrupting planetesimals motivate questions about the dynamical processes which break up asteroid-sized bodies around white dwarfs. Although previous theoretical work has focussed on modelling spherical bodies, observational evidence indicates that asteroids can be well modelled by triaxial ellipsoids.Here, we present an analytical framework which applies tidal, self-gravitational and internal strength forces to triaxial ellipsoids approaching a white dwarf on extremely eccentric (e ≈ 1) orbits. The subsequent disruption of the asteroids is split into three distinct regimes: tidal fragmentation, sublimation, and direct impact. This framework is extended to cover a simplified Main Belt analogue of 100 planetesimals with an observationally motivated size distribution and randomly chosen shape models and materials for a range of white dwarf temperatures.We find that using a spherical shape model consistently underestimates where sublimation occurs and overestimates the fragmentation distance. The small spatial scales of white dwarfs can cause these discrepancies to have a large effect on predicted observations of debris. Our results allow us to place constraints on the expected planetary debris from asteroids at different white dwarf cooling ages and motivates future studies to include more accurate shape models.