Thoracic aortic dissection is a dangerous pathological condition where blood intrudes into the vascular wall, creating an artificial channel, the false lumen. The weakened false lumen wall may rupture, resulting in high mortality. Biomechanical factors investigated are the size of the dissecting aneurysm, the blood pressure, the geometry around the distal tear, a configuration of partial thrombosis, the distance between the tears, and the shear stress. The force acting on the walls of the false lumen will generally become larger with increasing size of the dissection or a higher blood pressure. The effects of shear stress, in terms of the 'average wall shear stress' and 'oscillatory shear index', are elucidated, with low shear stress reversing in direction over time implying damage to the blood vessel. Clinicians can thus assess the danger of imminent rupture quantitatively. This information will help in the decision regarding surgical interventions.