Boundary-value problem of three-dimensional poroviscoelasticity is considered. The basic equations for fluid-saturated porous media proposed by Biot are modified by applying elastic-viscoelastic principle to classical linear elastic model of the solid skeleton. To describe viscoelastic properties of the solid skeleton model with weakly singular kernel is used. Boundary Integral Equations (BIE) method and Boundary-Element Method (BEM) with mixed discretization are applied to obtain numerical results. Solutions are obtained in Laplace domain. Modified Durbin's algorithm of numerical inversion of Laplace transform is used to perform solutions in time domain. An influence of viscoelastic parameter coefficient on dynamic responses is studied.