We propose a method to estimate the bending rigidity and Young's modulus of thin conducting suspended membranes based on measuring the deflection of the membranes submitted to an electrostatic force. Our electrostatic method appears easier to implement and more reliable than AFM-based localized force-displacement measurements to estimate the bending rigidity and Young's modulus of slightly inhomogeneous materials. We apply the method on suspended graphene oxide (GO) sheets coated with a 5 nm thick Ni layer, providing a demonstration of electrostatic actuation for GO sheets. For a 7.7 nm thick membrane, a Young modulus of 360 GPa is found.