Within a hydroelastic perspective and through a higher-order implementation, the performance of extended boundary integral equation method (EBIEM) for the removal of irregular frequencies that are inherent to the wave Green function based boundary element solution of the frequency domain wave-body interaction problems is investigated. The fundamental idea of the EBIEM is extending the computational domain by the assumed internal free surface, which is covered by a rigid lid to suppress the non-physical internal fluid motion. The EBIEM is expected to suppress the irregular frequencies completely, though higher-order applications often require a problem dependent analysis for an elimination through a wide frequency range. By focusing on the mesh fineness and element order and selecting two different surface piercing structures. a cylinder and a large floating plate. some general conclusions are drawn.