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Numerical finite element analysis (FEA) of a poly(vinylidene fluoride) (PVDF) flexural plate wave (FPW) acoustic gravimetric gas sensor is used to study the performance implications of a soft polymeric substrate with a stiffness comparable to the stiffness of the gas sensing layer. The low substrate stiffness allows small gas-absorption induced variations in sensing layer stiffness to have a significant impact on the resonance frequency of the device, enabling greatly improved stiffness sensitivity compared with mass-only models derived for sensors with stiffer substrates. Experimental results from sensors with poly(vinyl alcohol) (PVA) as the affinity layer show good agreement with the model. Further simulations show that the choice of film thickness and substrate tensioning provide mechanisms for tuning the device performance.