In this paper, a theoretical model of a micro-perforated panel (MPP) backed by a finite cavity and flush-mounted in an infinite baffle is developed and its performance in terms of sound absorption is analyzed. The model allows an oblique incidence sound impinging upon the MPP absorber. The simplified Rayleigh integral method, thin plate theory and the acoustical impedance of the MPP are used to calculate the sound energy absorbed by the MPP's surface. Results show that the absorption coefficient of the absorber is a function of angle and frequency of the incident sound, and is controlled by the coupling between the MPP and the acoustical modes in the back cavity. In particular, grazing modes can be induced in the cavity by sound with an oblique angle of incidence, which may result in peak sound absorptions at the natural frequencies of the modes. The mechanism involved is used to explain the absorption properties of the MPP absorber for a diffuse incidence of sound. © 2013 Acoustical Society of America.