The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of poroelastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on directapproach boundary integral equations of 3-D isotropic linear theory of poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods.