Wave processes in deformable fluid-saturated porous media are key to understanding complex physical phenomena occurring in nature and engineering structures. Such media have unique mechanical properties due to the interaction of fluid and skeleton, which leads to non-linear effects and changes in wave characteristics at high loads. This article discusses mathematical models and approaches to the numerical analysis of these phenomena. Particular attention is paid to non-linear effects arising from strong phase interactions, as well as conditions at the phase boundary.

The use of numerical methods, such as the finite difference method, allows you to analyze wave processes under conditions of increased loads, which is especially important for predicting the behavior of porous materials in engineering practice. Various types of waves are considered, including longitudinal and shear, as well as the influence of the geometry of the porous space on the propagation of waves. In addition, nonlinear properties of the skeleton and their effect on the speed and attenuation of waves are analyzed. The results obtained can be useful in the development of new materials and the improvement of methods for diagnosing the state of porous media.