Large deformations in a rubber bearing between two conical tubes may lead to squashing folds that can cause local rupture of the rubber followed by complete destruction of the bearing. A new method, CAO (computer-aided optimization), which is based on the simulation of biological growth, is used to avoid these squashing folds by reducing the notch stresses that occur even at small deformations. Although the shape optimization procedure is carried out for small deflections it is verified by a large-deflection finite-element method (FEM) run that, even in the case of the largest deformations, no squashing folds are formed in the optimized design.