In general vibration theories of thin elastic plate, the plates have been assumed to be nonpermeable. However, previous work on permeable membranes revealed that the acoustic properties of a membrane are strongly affected by its permeability [Takahashietal., J. Acoust. Soc. Am.99, 3003–3009 (1996)]. In this study, permeable elastic‐plate absorbers are proposed and their acoustic performance is examined by means of numerical analysis. For the simplest model, a theory for sound transmission through and sound reflection by a single permeable plate absorber with the oblique incidence of steady‐state plane wave is developed. In this theory, permeability of the plate is represented by unit‐depth flow resistivity [MKS‐rayl/m]. Subsequently, for more complex models, structured absorbers composed of the facing of a permeable plate and several layers of air and/or absorptive materials are investigated theoretically. With these theoretical models, parametric surveys are executed to evaluate the acoustic performance of permeable elastic‐plate absorbers. As a result of numerical calculations, it becomes clear that the flow resistance of the permeable elastic plate has a remarkable influence on its acoustic characteristics, especially at high frequencies.