A mathematical model was developed for the analysis of a fuel filler door with a torsional spring. The model calculates performance indices such as opening and closing forces, kinetic energy during opening and closing and the maximum spring stress. The model was integrated with an optimization program. Two types of optimization problems were formulated: the traditional problem which does not include the effects of random design parameters, and the stochastic type optimization, which does. An example shows how the mathematical model, in conjunction with optimization techniques, can help determine fuel filler door designs.