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The vibration performance of hermetically sealed electromagnetic relay which contains armature system is an important element when we judge the reliability of apparatus. A nonlinear single-degree-of-freedom mathematic model considering contact loss was built in this paper, and the dynamic behavior of armature subjected to external Gaussian white noise excitation was investigated by using Fokker-Planck equation and Monte Carlo simulation. Both the spectral contents and statistical results of the contact force showed great coincidence with reality. From the statistical results and spectral diagrams, the relation between the probability of loss contact, model parameters and system behavior was discussed, and the conclusions are of great importance for the reliability design of hermetically sealed electromagnetic relay.