The Helmholtz-Kirchhoff integral and the Kirchhoff approximation are applied to model the penetration of sound waves into rough sandy seafloors at grazing angles above and below the critical angle. As the seafloor of interest is anisotropic, emphasis is placed on simulating the response from a two-dimensional interface. The analytical development of the method is first presented, followed by numerical examples. Simulations and data acquired at sea are in very good agreement in the 2-15 kHz band [Maguer et al., J. Acoust. Soc. Am. 107, 1215-1225 (2000)]. The model predicts, in agreement with the 2-15 kHz acoustic data, the contributions due to roughness effects that dominate the evanescent wave component over most of this frequency band. Secondary effects such as coherent (Bragg) influence patterns and the loss of signal coherence with grazing angle or depth are correctly predicted. The model simulations strongly suggest that roughness of the sediment interface is most likely the cause of anomalous sound penetration into the seabed.