Based on the Porous Media Theory (PMT), a mathematical model of space-axisymmetrical problems for incompressible fluid-saturated visco-elastic porous media is presented in the case of small deformation, in which the differential-type constitutive relation is applied to describe the mechanical characteristics of solid skeleton. The differential quadrature method (DQM) and the second-order backward difference scheme are used to discretize the governing equations on the spatial and temporal domains, respectively, and a method is proposed to deal with the singularity conditions at points located on the symmetry axis. As application, the dynamic behavior of a column of fluid-saturated elastic porous media is analyzed firstly. The obtained results are compared with the analytical results in the existing literature, they are comparatively accordant, which means that the model and method presented in this paper are correct, and the obtained results are reliable. Further, the dynamic response of a space-axisymmetrical body of fluid-saturated visco-elastic porous media is analyzed, in which the material characteristic of the solid skeleton is described by Burgers model with four parameters.