Abstract: In the framework of porous media model developed from mixtures theories,an initial and boundary value problem is presented for one-dimensional dynamic response of porous media.Analytical solutions are obtained using Laplace transform and convolution theorem for the transient wave motion in saturated porous media under arbitrary stress boundary condition and displacement boundary condition,respectively.Through several illustrative numerical examples,the displacement and stress fields of solid skeleton as well as the velocity and pore pressure fields of interstitial fluid in transient wave motion under the two types of boundary conditions are discussed.It is demonstrated that the wave motion in saturated porous media is a coupled process of the waves in the skeleton and the interstitial fluid.The apparent visco-elasticity of saturated porous media is also discussed.