The objective of this article is to set forth a computationally efficient methodology to quantify the effects and assess the relevance of geometric and material uncertainty on a permanent magnet synchronous machine (PMSM), based on a nonlinear finite-element model (FEM). Our methodology follows the theory of Gaussian process regression and principal component analysis to build a computationally inexpensive surrogate model that replaces the FEM. Uncertainty quantification and sensitivity analysis studies focus on the electromagnetic torque, flux linkage, and core loss of the PMSM.