When a ship is running in following seas, the encounter frequency is reduced to a very low one. In that case broaching, surfiding and capsizing phenomena are most likely to occur due to wave exciting forces acting on a ship in following seas. In this paper, the emphasis is mainly laid upon transverse stability of ships following seas, which is related to capszing phenomenon. The authors take the case that ship speed is equal to the wave celerity, i.e., the encounter frequency is zero. Hydrostatic force and moment due to Froude-Krylov hypothesis are calculated by line intergral method. Transverse stability is evaluated from hydrostatic force and moment. Through the application of present calculation method to box-shaped vessel, it is confirmed that the transversestability of a vessel can be reduced to critical level at wave crest.