This work presents a mixed finite element formulation for modelling solid–fluid interaction within a fully saturated porous media, motivated by the numerical challenges encountered when simulating biological tissues such as the intervertebral disc (IVD) under transient loading. Abrupt acceleration and deceleration of fluid flow can lead to non-physical pressure oscillations and numerical instabilities which limit the reliability of standard low-order formulations. This model, implemented in the open-source parallel finite element library MoFEM has a diverse range of potential applications including geotechnical engineering, geophysics and biomechanics. A linear poroelastic framework is adopted in which displacement, fluid pressure, and fluid flux are treated as independent fields. This mixed formulation is essential for avoiding pressure oscillations that arise when pressure is approximated in the H^1 Sobolev space. In contrast to the standard formulation, fluid flux is approximated as an independent field in the H(div) (Raviart-Thomas) space, which ensures the continuity of normal flux, while pressure is approximated in the discontinuous L^2 Lebesgue space. High-order finite element approximations implemented within the MoFEM framework are employed to mitigate the locking phenomenon observed in poroelastic problems. This can occur through a combination of low permeability and near-incompressible fluid response and can lead to numerical instability and loss of solution accuracy. The proposed formulation is validated against analytical benchmarks such as that of Terzaghi, confirming the robustness and numerical stability of the mixed formulation, particularly in reducing non-physical pressure oscillations under transient flow conditions. The validated framework is subsequently applied to biomedical engineering problems, illustrating its suitability for simulating the compression of the IVD. Observed oscillatory responses under highly transient loading conditions motivate current investigation into hybridised multi-grid formulations to further improve numerical stability and robustness.