This paper deals with a theoretical study of the sound absorption characteristics of a membrane-type sound absorber. A closed-form analytical solution for the sound absorption coefficient of an infinite membrane with an air-back cavity is produced by making a minor modification to the solution for a cavitybacked infinite elastic plate which was derived in the previous paper. To analyse the mechanism of absorption, the solution is rearranged in a form which points out the contribution of each element of a membrane-type sound absorber. The contribution of the cavity is found to be dominant, and that of the absorptivity of the source side surface of the membrane is rather small. In the case of an elastic plate, the contribution of the loss factor is found negligible. The effects of the parameters of the sound absorption system are discussed in the light of calculated results. Furthermore, the method to predict the peak-frequency and the peak value of the oblique-incident absorption coefficient of the membrane-type sound absorber is presented. The method satisfactorily explains the relationship between the absorption characteristics and the parameters. It is also applicable to panel absorbers. It can be useful for the design of the purpose-made membrane-type or panel absorbers, and for the sound field prediction within boundaries made from this type of absorber.