Electrical machines that are produced in mass production suffer from stochastic deviations introduced during the production process. These variations can cause undesired and unanticipated side-effects. Until now, only worst case analysis andMonte-Carlo simulation have been used to predict such stochastic effects and reduce their influence on the machine behavior. However, these methods have proven to be either inaccurate or very slow. This paper presents the application of a polynomialchaosmeta-modeling at the example of stochastically varying stator deformations in a permanent-magnet synchronous machine. The applied methodology allows a faster or more accurate uncertainty propagation with the benefit of a zero-cost calculation ofsensitivity indices, eventually enabling an easier creation of stochastic insensitive, hence robust designs.