In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modeling domain. The Bayliss, Gunzberger and Turkel (BGT) boundary dampers (1982), which require a circular cylindrical truncation boundary in the diffraction-radiation problem of water waves, have been particularly successful in this task. However, for an elongated body, an elliptic truncation boundary has the potential to reduce the modeling domain and hence the computational effort. Lee et al (1990), based on the pseudo-differential operator approach put forward by Engquist and Majda (1977), derived a second order absorbing boundary condition for an elliptic boundary equivalent to the BGT damper and used it in electromagnetic wave scattering problems by the finite difference method. In this paper, this boundary condition is implemented in the form of a boundary damper approximation in the context of the finite element method and used in solving water wave radiati on of a floating body. The efficacy of this approach for diffraction problem has recently been demonstrated by Bhattacharyya et al (2000). The performance of the damper on elliptic truncation boundary is established using an example of radiation by a floating semi-ellipsoid by studying its hydrodynamic added mass and damping coefficients.