In a certain kind of eye surgery, the human eyeball is deformed sustainably by the applicationof an elastic band. This article presents a mathematical model for the mechanics of the combinedeye/band structure along with an algorithm to compute the model solutions. These predict the immediateand the lasting indentation of the eyeball. The model is derived from basic physical principles byminimizing a potential energy subject to a volume constraint. Assuming spherical symmetries thisleads to a two point boundary value problem for a nonlinear second order ordinary differential equationthat describes the minimizing static equilibrium. By comparison with laboratory data, a preliminaryvalidation of the model is given.