In engineering practice, a cover layer of coarser material has been used to protect a buried marine pipeline from wave-induced seabed instability. However, most previous investigations of the wave-seabed-pipe interaction problem have been concerned only with such a problem either in an isotropic single layer or a rigid pipe. This paper proposes a two-dimensional finite element model by employing the principle of repeatability to investigate the wave-induced soil response around a buried pipeline. The elastic anisotropic soil bahavior and geometry of cover layer are included in the present model, while the pipe is considered to be an elastic medium. This study focuses on the effects of a cover layer (including thickness B and width W of the cover layer) on the wave-induced pore pressure in the vicinity of a buried pipeline.