An analytical model based on the low reduced-frequency method is developed for the damping and spring force coefficients of micro-electro-mechanical systems (MEMS) structures. The model is based on a full-plate approach that includes thermal and viscous losses and hole end effects, as well as inertial and compressibility effects. Explicit analytical formulas are derived for damping and spring forces of perforated circular MEMS with open and closed edge boundary conditions. A thermo-viscous finite-element method (FEM) model is also developed for the numerical solution of the problem. Results for the damping and spring coefficients from the analytical models are in good agreement with the FEM results over a large range of frequencies and parameters. The analytic formulas obtained for the damping and spring coefficients provide a useful tool for the design and optimization of perforated MEMS. Specifically, it is shown that for a fixed perforation ratio of the back-plate the radius of the holes can be optimized to minimize the damping.