The successful modelling of the mechanical properties of mineralized tissues depends critically on the knowledge of the off-axis behaviour of individual unidirectional lamellae. Information on this is lacking. In this work we attempt to rectify the situation. Young's modulus, measured in bending and tension, and the tensile strength and ultimate strain to failure of the dentine of the narwhal Monodon monoceros, were determined on specimens that had almost unidirectional fibres, whose direction differed considerably from specimen to specimen. Modulus and strength decreased steadily with the degree of off-angle loading, falling to about 45% of maximum for modulus, and 35% of maximum for strength. Ultimate strain showed a less uniform behaviour, and remained remarkably high at large angles. Differences in mechanical behaviour were not related to the very small differences in mineral content measured between specimens. These findings have strong implications for modelling the anisotropic behaviour of bone, because dentine is very much like bone in most important respects. Predictions using classical composite theory are reasonably satisfactory, as long as the mineral crystals are assumed to be platelets, not rods.