The so-called strip theory is widely used for calculation of wave exciting forces. But it has been recognized that the numerical result obtained by the strip theory loses the accuracy when the encounter frequency gets very low in following waves. It is known that the broaching-to phenomenon takes place in that circumstance. However, the existing method does not succeed in predicting with enough accuracy the wave exciting yaw moment which is deemed as the main cause of the broating-to phenomenon. In the present paper, a theoretical method is described for calculating the diffraction force acting on a ship travelling in following waves at high speed. Yamasaki et al. applied Chapman's theory to manoeuvring problem, and in this paper the method adopted by them is extended to the diffraction problem. Numerical computations using the present method are carried out and compared with the experiments of wave exciting forces in order to verify its validity. Then it is concluded that this method gives closer results to the experiments than the strip theory and that it can be used for solution of the diffraction problem at very low encounter frequency. Furthermore, numerical values of wave exciting yaw moment obtained by the present method are presented in order to clarify the relation between the magnitude of yaw moment and the position of a ship on the wave surface, travelling in following waves at a low encounter frequency. Then it proves that the magnitude of wave exciting yaw moment becomes maximum when a ship is located on the down slope of the incident wave.