We describe sensing of chemical vapors from the atmosphere using critically buckled polycrystalline silicon doubly clamped mechanical resonators coated on one side with polymethyl methacrylate (PMMA). Our method of sensing is based on stress-induced resonance frequency shifts through volumetric swelling of the 60 nm thick PMMA layer resulting in altered tension in the beams. The stress change produces shifts in the resonance frequency as large as 150 of the baseline frequency. In order to maximize the sensitivity, we tailor residual stress of the polycrystalline silicon resonators to slightly exceed the critical buckling stress. We incorporate a relatively large gap between the bridge and a substrate to provide optical readout and minimize squeezed film effects. We show that the larger gap results in substantial improvements of the quality factor and frequency stability of our resonators under ambient pressure and temperature conditions compared to previous implementations. These lead to resonance frequency shift per concentration change of ethanol vapors of ∼360 Hz/ppm with a response time of a few seconds measured in our gas delivery and readout system.