We present a practical method to evaluate gas permeability for thin polymer films using an encapsulated micro-electro-mechanical-system (MEMS) oscillator. Previously, we have developed a hermetic thin-film dome structure for RF-MEMS tunable capacitor, using conventional back-end-of-the-line (BEOL) processes. The dome is made of multiple layers including a polymer film, whose gas permeability is an important factor with respect to productivity and reliability. So far, it had been difficult to evaluate the gas permeability for such small and thin polymer films with sub-millimeter diameter and micron-scale thickness. In this evaluation method, the pressure dependence of air-damping oscillation is used to measure the permeability. As a demonstration, we carried out a permeability measurement of a 0.5-mm-diameter dome sealed with a thin (1 μm) polymer film. The resulting permeability coefficient is found to be 1×10 -16 mol/m/Pa/s, at room temperature.