Thermoelastic damping and fluid damping may collectively affect the resonant behaviors of silicon resonators. A finite element model is developed to predict the characteristics of the out-of-plane resonance, and the results are verified by experiments. The implementation of the perturbation method leads to an eigenvalue equation, from which the resonant frequency and the quality factor can be evaluated. The fluid damping problem is formulated by augmenting the governing equation with a linear damping term, whose coefficient is inversely determined from the experimental correlations. With the incorporation of the fluid damping term, the computational prediction achieves a good agreement with the experiment. The same method can also be extended to study the in-plane vibration of beam resonators.