Boundary-value problems for piecewise homogeneous solids in terms of linear three-dimensional poroviscoelasticity are considered. Mathematical model of poroviscoelastic material is based on Biot's model of poroelasticity. Viscoelastic effects refer to a skeleton of porous material and are described through the correspondence principle. Standard linear solid model is employed. Viscosity parameter influence on dynamic responses of displacements, pore pressure and tractions is studied. In order to study the boundary-value problem boundary integral equations (BIEs) method is applied, and to find their solutions boundary element method (BEM) for obtaining numerical solutions is used. The numerical scheme is based on the Green-Betty-Somilliana formula. The solution of the original problem is constructed in Laplace transforms, with the subsequent application of the algorithm for numerical inversion. Modified Durbin’s algorithm of numerical inversion of Laplace transform is applied to perform solution in time domain. The problem a poroviscoelastic prismatic solid clamped from one end and free at another is considered. The solid is composed of two subdomains. Heaviside-type load is applied to a free end of the solid. Numerical results for displacements and pore pressure, when subdomains are modelled with different viscoelastic properties, are presented.