An analytical model for the damping and spring force coefficients of micro-electro-mechanical systems (MEMS) with a flexible diaphragm is developed. The model is based on the low reduced-frequency method, which includes thermal and viscous losses as well as inertial and compressibility effects. Specifically, the solutions are derived for circular MEMS with a clamped diaphragm with both open-edge and closed-edge boundaries. The deflection function of the circular clamped diaphragm is incorporated into the thermoviscous acoustic (TA) formulation to take into account the effect of the flexibility of the diaphragm. TA finite-element analysis (FEA) is also used to develop a computational model. The analytical results are in good agreement with the FEA results for a wide range of parameters and frequencies. The significance of the effect of the flexibility of the diaphragm on damping for actual MEMS is demonstrated. Measurements of the damping coefficient of circular MEMS are conducted for experimental validation of the presented model. The small difference between the experimental results and the results from the model (less than 6%) validates the accuracy of the presented model. The proposed analytical model can be applied to MEMS with various geometries and boundary conditions.