Vesicles are small cell-like compartments formed by amphiphilic molecules in solution. They are principally studied for their ubiquitous role in biology, but are also important to commercial areas of research, such as cosmetics, drug-delivery and agriculture. The dynamical behaviour of vesicles is very complicated and the morphology which is observed is poorly understood. \par A model is presented which uses linear non-equilibrium thermodynamics to reduce questions of stability to problems which are geometrical in nature. The stability of growing vesicles is then examined and a physical interpretation of the results is provided.