Non-stationary acceleration waves in the fluid-saturated inhomogeneous elastoviscoplastic porous medium are studied using the mathematical theory of discontinuities. The equations for determining the intensity and the geometry of wave fronts of the fluidsaturated elastoviscoplastic medium were first derived. It is shown that in the medium under consideration there are two types of irrotational waves and one equivoluminal wave, that are equal to the velocities in the homogeneous elastic porous media at every point
