Based on the theory of porous media, a general Gurtin variational principle for the initial boundary value problem of dynamical response of fluid-saturated elastic porous media is developed by assuming infinitesimal deformation and incompressible constitutes of solid and fluid phase. The finite element formulation based on this variational principle is also derived. As functional of the variational principle is a spatial integral of the convolution formulation, the general finite element discretization in space results in symmetrical differential-integral equations in time domain. In some situations, the differential-integral equations can be reduced to symmetrical differential equations, and, as an numerical example, it is employed to analyze the reflection of one-dimensional longitudinal wave in a fluid-saturated porous solid. The numerical results can provide the further understanding of the wave propagation in porous media.