The exact nonlinear differential equations of motion for free symmetric vibration of a circular membrane have been derived and solved, approximately, by a perturbation procedure and the Ritz‐Galerkin technique. The resulting Duffing equation with a hardening‐spring characteristic for the fundamental mode of the membrane was solved for the ratio of the nonlinear to linear period of free vibration. Theoretical expressions for air virtual mass, damping, and the nonlinear spring stiffness were used to obtain an approximate solution to sinusoidal excitation of the membrane. The results from an experimental program for sinusoidal acoustic excitation of a nonlinear circular membrane have been presented. Construction of the membrane fixtures and a capacitance‐type transducer used for transient‐ and frequency‐response displacement measurements on several Mylar and aluminum membranes is described. Experimental data on the air virtual mass, frequency response at various ambient air pressures, dynamic mode shape, and damping are shown. The theoretically derived “backbone” curves of the Duffing‐equation frequency response appeared to be in very good agreement with the experimental data. The damping was found to be nonlinear, with some indications of being nonviscous as well.