The fully coupled, porous solid-fluid dynamic field equations with u−p formulation are used in this paper to simulate pore fluid and solid skeleton responses. The present formulation uses physical damping, which dissipates energy by velocity proportional damping. The proposed damping model takes into account the interaction of pore fluid and solid skeleton. The paper focuses on formulation and implementation of Time Discontinuous Galerkin (TDG) methods for soil dynamics in the case of fully saturated soil. This method uses both the displacements and velocities as basic unknowns and approximates them through piecewise linear functions which are continuous in space and discontinuous in time. This leads to stable and third-order accurate solution algorithms for ordinary differential equations. Numerical results using the time-discontinuous Galerkin FEM are compared with results using a conventional central difference, Houbolt, Wilson θ, HHT-α, and Newmark methods. This comparison reveals that the time-discontinuous Galerkin FEM is more stable and more accurate than these traditional methods.