When travelling in heavy following sea a ship is accelerated on the front slope of a wave and her velocity may become nearly the same as the wave celerity. This phenomenon is called surf-riding and may cause broaching-to, which is very dangerous situation for small craft. The present paper relates to the surf-riding. First, the resistance variation in wave, an important factor of the surf-riding, was treated with both theoretically and experimentally. The usefulness of theory on the Froude-Krylov hypothesis was examined by the proposed theoretical method on the boundary value problem and the captive model experiments. Second, the motion involving the surf-riding phenomenon was realized and recorded in a towing tank. The results show a fairly good agreement with a digital simulation based upon the theory and captive model experiments. Finally the author proposed a diagram indicating the possibility of surf-riding for a given wave and ship on the basis of the present studies. This simulation study proved useful to predict surf-riding of a given ship.