Modelling of porous media has a wide range of applications in, for example, soil mechanics, chemical engineering, civil engineering, biomechanics and aerospace engineering. A big challenge in modelling multiphasic porous material lies in the process of accurately capturing the physics behind the interactions between the various phases. A thermodynamic consistent modelling approach is given by the theory of mixtures combined with the concept of volume fraction, called the theory of porous media (TPM). Within the framework of TPM, the dynamical behavior of multi phasic porous material is described using coupled nonlinear partial differential equations [1]. Besides earthquake engineering, understanding dynamics of porous media is also useful in structural and acoustical engineering, where such media provide essential damping and absorption properties. A simple case of one-dimensional fully saturated porous media problem has been analytically solved for forced excitation using Laplace transform for an infinite domain, see [2], and using Laplace transform and power series expansion for a finite domain, see [3]. High-fidelity numerical solutions are often computationally expensive and thus not effective for iterative design optimization process. Real-time applications such as active vibration isolation also require swift model-response. Model-order reduction techniques such as asymptotic analysis overcome such challenges. [4]. Using a nondimensionalized modelling approach, a parameter study is conducted to highlight the effects of various input parameters on the dynamics of one-dimensional biphasic poroelastic media. Asymptotic analysis is further applied in limit regimes of these parameters to reduce the complexity of the model. A finite difference scheme is used to validate and verify the solution procedure. Applications in aerospace engineering are also discussed.