In this paper, based on Biot's theory, a numerical model for wave-seabed-pipeline dynamic response was established to investigate seabed instability failure. The seabed was treated as porous medium. The model simulated the distribution of pore pressure and effective stress, and the process of liquefaction around buried pipeline under various wave loads were investigated. Partly dynamic (u-p) formulations for the wave-induced response of the seabed with pipeline were adopted. In partly dynamic analysis, the u-p formulation in which both displacement and pore pressure were field variables was adopted considering the acceleration of soil skeleton while neglecting the inertial terms associated with pore water. Using COMSOL Multiphysics, a parametric study, including the permeability, degree of saturation, buried depth and wave height was conducted to investigate the seabed response. Then, a criterion for liquefied state was used and the possibility of wave-induced liquefaction occurring in porous seabed was studied.