Ferroelectric materials based on lead zirconate titanate (PZT) are widely used as sensors and actuators because of their strong piezoelectric activity. However, their application is limited because of the high processing temperature, brittleness, lack of conformal deposition, and a limited possibility to be integrated with the microelectromechanical systems (MEMS). Recent studies on the piezoelectricity in the 2-D materials have demonstrated their potential in these applications, essentially due to their flexibility and integrability with the MEMS. In this work, we deposited a few layer graphene (FLG) on the amorphous oxidized Si3N4 membranes and studied their piezoelectric response by sensitive laser interferometry and rigorous finite-element modeling (FEM) analysis. Modal analysis by FEM and comparison with the experimental results show that the driving force for the piezoelectric-like response can be a polar interface layer formed between the residual oxygen in Si3N4 and the FLG. The response was about 14 nm/V at resonance and could be further enhanced by adjusting the geometry of the device. These phenomena are fully consistent with the earlier piezoresponse force microscopy (PFM) observations of the piezoelectricity of the graphene on SiO2 and open up an avenue for using graphene-coated structures in the MEMS.