This paper focuses on the variability in vibration from electromagnetic origin for an electric motor. The multiphysics modeling is introduced by the magnetic force density computation and by the coupling of the 2D electromagnetic and 3D structural dynamic finite element models. The modal stability procedure (MSP) and the Monte Carlo Simulation (MCS) are associated for the variability calculation of natural frequencies and frequency response functions (FRFs) of finite element systems with material random parameters. The MSP formulations are developed for 8-node solid hexahedron element modeling the electric stator. The MCS–MSP approach only requires a single finite element analysis, leading to a fast Monte Carlo simulation using MSP formulation. The validation of MCS-MSP is investigated, the uncertainty propagation is discussed and the computational costs of MCS-MSP are presented. This non-intrusive method provides an evaluation of frequencies and FRFs variability for industrial-size models with a large number of degrees of freedom, a large number of random variables and a low or moderate variability level.