Light scattering and electron microscopy have been utilized in some research in order to study the transition induced by adding surfactant to the aqueous solution of small liposome vesicles. Using the theory of elastic membranes to describe the mixed bilayer of the liposome, an extensive deformation analysis of the enlarged vesicle is reported in the present work. An investigation of pressure versus radius reveals the existence of stable and unstable configurations of equilibrium. From obeservation of the Total Potential Energy function, the instability is recognized and discussed in detail. Besides its value in explaining some very interesting phenomena observed in the experimental study of liposomes in the presence of surfactant, the analysis presented in this paper can be useful in pointing out a way to predict the surfactant critical concentration when the liposome breaks into micelles. This rupture is an undesired phenomenon since the liposomes can be used to transport drugs.