Vesicles prepared by extrusion are closed membrane systems commonly used as models for more complex biological membranes, and which have pharmaceutical applications as vessels for drug delivery. In this thesis, theoretical and experimental investigations of static and dynamic light scattering reveal limitations of these techniques and the conditions required in order to unambiguously characterize both the size distributions and morphologies of extruded vesicles. Similar investigations of small angle neutron scattering (SANS) measurements of vesicle membrane thickness reveal analogous limitations of this technique. A new analysis method for the determination of membrane thickness from SANS measurements is also introduced and tested. These investigations form the basis for modelling and experimental measurements of osmotically induced shape changes to vesicles. Our measurements, which are interpreted within the Area Difference Elasticity model (Jaric,? et. al. 1995. Phys. Rev. E. 52: 6623-6634) for membrane curvature, reveal significant differences in the shape behaviour and associated mechanical properties of membranes composed of dioleoylphosphatidylchohne and stearyloleoylphosphatidylcholine.