The coupled mode (CM) and finite-element methods (FEMs) are developed and used to predict the acoustic reflection coefficient of a semi-infinite porous medium with closely spaced two-dimensional (2D) periodical corrugations. These methods are also applied to predict the reflection coefficient of a periodic array of porous corrugations installed on an acoustically rigid surface. It is shown that the predictions by the both methods agree closely. The reflection coefficient and Brewster angle of total refraction for the corrugated semi-infinite medium predicted with these methods are compared against that predicted by the Biot/Tolstoy/Howe/Twersky and extended Twersky models. A similar analysis is carried out for porous corrugations set on a rigid backing. The behavior of the reflection coefficient and the pole in the expression for the reflection coefficient located close to grazing incidence is studied.