This article presents a methodology for the treatment of uncertainty in nonlinear, interference-fit, stress analysis problems arising from manufacturing tolerances. Image decomposition is applied to the uncertain stress field to produce a small number of shape descriptors that allow for variability in the location of high-stress points when geometric parameters (dimensions) are changed within tolerance ranges. A meta-model, in this case based on the polynomial chaos expansion, is trained using a full finite element model to provide a mapping from input geometric parameters to output shape descriptors. Global sensitivity analysis using Sobol’s indices provides a design tool that enables the influence of each input parameter on the observed variances of the outputs to be quantified. The methodology is illustrated by a simplified practical design problem in the manufacture of automotive wheels.