  We derive and study a new hyperbolic two-phase model of a porous deformable
medium saturated by a viscous fluid. The governing equations of the model are
derived in the framework of Symmetric Hyperbolic Thermodynamically Compatible
(SHTC) systems and by generalizing the unified hyperbolic model of continuum
fluid and solid mechanics. Similarly to the unified model, the presented model
takes into account the viscosity of the saturating fluid through a hyperbolic
reformulation. The model accounts for such dissipative mechanisms as
interfacial friction and viscous dissipation of the saturated fluid. Using the
presented nonlinear finite-strain SHTC model, the governing equations for the
propagation of small-amplitude waves in a porous medium saturated with a
viscous fluid are derived. As in the conventional Biot theory of porous media,
three types of waves can be found: fast and slow compression waves and shear
waves. It turns out that the shear wave attenuates rapidly due to the viscosity
of the saturating fluid, and this wave is difficult to see in typical test
cases. However, some test cases are presented in which shear waves can be
observed in the vicinity of interfaces between regions with different porosity.
