Dynamic behavior of poroviscoelastic solids is studied in this paper. Poroviscoelastic problem formulation is based on Biot.s theory of poroelasticity. In order to describe viscous properties of skeleton by means of the correspondence principle such classical viscoelastic models are used: Kelvin-Voigt model, standard linear solid and model with weakly singular kernel. A numerical modelling of wave propagation is done by means of boundary element approach. Boundary element method (BEM) and boundary integral equation (BIE) method are applied to solving three-dimensional boundary-value problems. Solution is obtained in Laplace domain. Numerical inversion of Laplace transform is based on Durbin.s method with variable integration step and Runge-Kutta relying method. Results of numerical experiments are given