This paper presents a complete model for analysis of the deformed shape of a prestressed circular axisymmetric membrane of a liquid lens. The governing equations are derived using the exact relation between displacements and the Green-Lagrange strains combined with the Saint Venant-Kirchhoff material law, which postulates a linear relation between the Green-Lagrange strains and the second Piola-Kirchoff stresses. A numerical solution based on minimization of potential energy is illustrated by an example, and the dependence of the maximum membrane deflection on material properties and initial prestress is analyzed. The theoretical model is then experimentally validated. It is shown that the model is suitable for large-strain analysis of liquid lens membranes and provides sufficiently accurate results that can be used in further analyses and simulations of imaging properties of active optical elements based on liquid lenses.