The subject of the wave-seabed-structure interaction is important for geotechnical and coastal engineering regarding stability analysis of foundations for offshore structures. Most previous theoretical investigations available concerned only with such a pipeline in a uniform single layer seabed. In this paper, a wave-seabed-pipeline system is modeled using finite elements. The seabed is treated as porous medium and characterized by Biot's dynamic equations. To explore the mechanism of the seabed instability, the two possible formulations: partly dynamic (u-p model) and fully dynamic (u-w model) for the wave-induced seabed response are considered. Verification of the proposed model is performed against the previous analytical result and experimental data. Based on the numerical results, the effects of wave and seabed characteristics, such as water depth, permeability, shear modulus, degree of saturation, and pipeline buried depth, on the wave-induced excess pore pressure and vertical effective stress will be examined. Finally, a parametric study will be conducted to examine the effects of wave and soil characteristics on the liquefaction potential. It is worth noting that soil permeability has a very significant influence on the pore pressure generation and liquefaction.