Objective: To use finite element modelling to look at the impact of lumen shape and vessel geometry on stress distribution in a vessel. Methods: A finite element model of an atherosclerotic plaque in a coronary artery was created and a non-linear analysis with Ogden strain energy function was done. The three most common shapes seen in an artery with an eccentric plaque-namely an elliptical lumen inside a circular vessel (A), a circular lumen inside an elliptical vessel, typical of a vessel with positive remodelling (B), and a circular lumen inside a circular vessel (C)-were modelled with and without lipid. Stress was analysed in the region of the fibrous cap separating the lumen from the plaque and the region of maximum stress along the circumference of the lumen was noted. Results: In a normal circular shaped coronary artery, the haemodynamic stresses were uniformly distributed all around the circle. However, if the circle was changed to an ellipse, the stresses were redistributed along the major axis and dropped substantially along the minor axis. The stresses in a positively remodelled vessel (B) were significantly greater than in A and C, by almost 100%. Moreover, the haemodynamic stresses increased significantly towards the major axis or the shoulder in A and B, due to lumen shape and vessel geometry alone, even in the absence of lipid in the model. The stresses also had a direct relation with the thickness of the lipid pool and an inverse relation with cap thickness and lumen stenosis. Conclusions: The increased vulnerability of the shoulder region of a plaque and a remodelled coronary artery are due, apart from other factors, to increased biomechanical stresses as a result of lumen shape and vessel geometry.