Lipid membrane is a continuous barrier between cell and organelle, providing relatively separate room for the vital biological reaction to take place and guarantee substance, energy and information exchange between cells and organelles. Helfrich proposed a spontaneous curvature model to describe the free energy of lipid bilayer. This article reviews the equations describing the equilibrium morphologies of closed lipid membranes and lipid membranes with free edge based on the spontaneous model, and some analytic solutions are provided as well. The practicality of proving linking condition for splitting vesicle is also discussed.