The propagation characteristics of surface transverse waves (STW) in polymer-coated surface gratings on rotated Y-cut quartz substrates are studied theoretically. A two-layer Love wave theory is combined with Floquet analysis to derive the wave dispersion and attenuation. The thickness of the polymer layer is found to affect the position and width of the frequency stop band, while the polymer viscosity introduces out-of-band attenuation. Both parameters effectively act in the vicinity of the lower-stop-band edge where STW resonators are mostly operated. The presented algorithm is applicable to the analysis of STW gas sensors and to the improvement of the resonator performance.