SUMMARYFin whales have an incompliant aorta, which, we hypothesize, represents an adaptation to large, depth-induced variations in arterial transmural pressures. We hypothesize these variations arise from a limited ability of tissues to respond to rapid changes in ambient ocean pressures during a dive. We tested this hypothesis by measuring arterial mechanics experimentally and modelling arterial transmural pressures mathematically. The mechanical properties of mammalian arteries reflect the physiological loads they experience, so we examined a wide range of fin whale arteries. All arteries had abundant adventitial collagen that was usually recruited at very low stretches and inflation pressures (2-3kPa), making arterial diameter largely independent of transmural pressure. Arteries withstood significant negative transmural pressures (−7 to −50kPa) before collapsing. Collapse was resisted by recruitment of adventitial collagen at very low stretches. These findings are compatible with the hypothesis of depth-induced variation of arterial transmural pressure. Because transmural pressures depend on thoracic pressures, we modelled the thorax of a diving fin whale to assess the likelihood of significant variation in transmural pressures. The model predicted that deformation of the thorax body wall and diaphragm could not always equalize thoracic and ambient pressures because of asymmetrical conditions on dive descent and ascent. Redistribution of blood could partially compensate for asymmetrical conditions, but inertial and viscoelastic lag necessarily limits tissue response rates. Without pressure equilibrium, particularly when ambient pressures change rapidly, internal pressure gradients will develop and expose arteries to transient pressure fluctuations, but with minimal hemodynamic consequence due to their low compliance.