A new hyperbolic two-phase model of a porous deformable medium saturated with a viscous fluid is presented and some of its features or performances are discussed. The governing equations are derived in the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems. The model accounts for such dissipative mechanisms as interfacial friction and viscous dissipation of the saturating fluid. Both dissipative mechanisms are modeled with hyperbolic equations with relaxation type source terms. The linearized version of the presented model is derived under the assumption of instantaneous relaxation of the phase pressures and its application to modeling propagation of small-amplitude waves in a porous medium saturated with a viscous fluid is discussed. We observe that accounting of the fluid viscosity may significantly affect the dispersion of fast and slow compression waves. Additionally, the shear wave attenuates rapidly due to the viscosity of the saturating fluid which makes it difficult to observe this wave in most of the test cases presented. However, some test cases are presented in which shear waves can be observed in the vicinity of interfaces between regions with different porosity.