This article is the logical continuation of a previous article (O. Coussy and T. Bourbié, 1984) concerning the propagation, within the framework of Biot's theory, of acoustic waves in infinite saturated porous media. Starting from the same assumptions as O. Coussy and T. Bourbié concerning the propagation media, this article analyzes the influence of the presence of plane geometric discontinuities (free semi-infinite media or the contacts between two semi-infinite media) or discontinuities with cylindrical symmetry (wells). After reviewing the stress-strain relations for a porous medium and the basic equations for dynamic poroelasticity, the article discusses the boundary conditions to be imposed on the interfaces. It then examines the general laws of reflection and refraction in poroelasticity (generalized Snell-Descartes laws). The application of these laws to several interesting specific cases mainly reveals the following phenomena: (1) a slow compressive wave is always generated at the interface between two saturated porous media; (2) the reflected and transmitted waves are generally inhomogeneous. In the next phase the propagation of acoustic waves is examined on the free surface of a semi-infinite saturated porous medium (Rayleigh waves) and at the plane interface between a liquid and a saturated porous medium (Stoneley waves). Compared to the properties known for them in conventional elastodynamics, these waves in poroelasticity are slightly dispersive, and appreciably attenuated because of the two-phase nature of the propagation medium. Lastly, the influence of a submerged source emitting near a permeable interface is examined. Emphasis is placed on the fundamental role of permeability and flow conditions at interfaces on the attenuation of S waves and surface waves. By way of comparison, the influence of these parameters on the first arrivals (P waves) is negligible. Likewise, it is shown that the geometry of the propagation medium plays a relatively secondary role. © IFP 1986