The vibro-acoustic performance of a rectangular double-panel partition with enclosed air cavity and simply mounted on an infinite acoustic rigid baffle is investigated analytically. The sound velocity potential method rather than the commonly used cavity modal function method is employed, which possesses good expandability and has significant implications for further vibro-acoustic investigations. The simply supported boundary condition is accounted for by using the method of modal function and the double Fourier series solutions are obtained to characterize the vibro-acoustic behaviors of the structure. The results for sound transmission loss, panel vibration level, and sound pressure level are presented to explore the physical mechanisms of sound energy penetration across the finite double-panel partition. Specifically, focus is placed on the influence of several key system parameters on sound transmission including the thickness of air cavity, structural dimensions, and the elevation angle and azimuth angle of the incidence sound. Further extensions of the sound velocity potential method to typical framed double-panel structures are also proposed.