The evaluation of wave-induced pore pressures and effective stresses in a poroelastic seabed is important for coastal and ocean engineers in the design of marine structures. Most previous theoretical investigations have focused commonly on the Stokes wave induced seabed response. In this paper, a cnoidal wave–seabed–pipeline system is modeled using the finite element method. Taylor’s expression and the precise integration method are used to estimate the Jacobian elliptic function. The seabed is treated as a poroelastic medium and is characterized by Biot’s partly dynamic equations (u–p model). The pore water pressure and effective vertical stress on the poroelastic seabed around a buried pipeline are examined. Based on the numerical results, a parametric study is conducted to examine the effects of wave and seabed characteristics on the seabed response. Comparison with the cnodial wave and Stokes wave induced seabed response is also demonstrated here. It implies that the difference between the maximum pore pressure and vertical effective stress induced by the cnoidal wave and Stokes wave may reach 60–70%.