The frequency-domain Rankine panel methods, which were developed by many researchers around 1990, have been applied to the seakeeping estimation of actual ships. However there still remains an unsettled problem on the numerical treatment of the infinite condition in the low-speed/low-frequency range and it prevents us using the method in the wide frequency region such as in oblique waves. In this paper, we employ two methods which are expected to settle the problem and make the Rankine panel method more useful. One is to introduce the Rayleigh’s artificial friction coefficient and another is to impose the juncture condition on the artificial control surface far from the ship. The former is originated in Yasukawa’s method²⁾ and the later is presented by one of the authors⁸⁾ extending the method proposed by Das et al.⁶⁾ and Yuan et al.⁷⁾ Experiments are also carried out in following wave condition and for zero forward-speed case, and compared with numerical results obtained by two methods. It is confirmed that both methods give accurate estimations in the low-speed/low-frequency range and the later method is especially better in accuracy.