The surface density or mass per unit area of a membrane is an important material property often used in acoustics and ultrasonics. In this paper, a new measurement and analysis technique for estimating the surface density as a function of frequency for a nonporous membrane or foil is introduced. This new, broadband technique is derived from the Thompson-Gray measurement model which can be simplified to the fluid layer transfer function commonly used in acoustics. The fluid layer transfer function can be further simplified to the limp-wall mass law for acoustically 'thin' membranes whose thickness is much less than a wavelength. The transfer function of the membrane can be efficiently measured with commercially available air-coupled ultrasonic transducers from which the surface density can be computed. Surface density estimates are presented for four membrane-like materials: aluminum foil, brass shim, polyester and polyethylene sheets.