Surf-riding phenomenon of a ship in regular following waves is examined. Results of the self-running model tests in the regular following waves with more than 300 runs show that there exists a definite critical condition in occurrence of the so-called surf-riding phenomenon which is clearly distinguished from the large amplitude surge motion, and that the critical condition can be regarded as the moment when the ship speed including the variable component due to the surge motion reaches the wave speed. Analytical considerations of equation of surging motion in following waves explain the above critical condition by the fact that once the ship speed reaches the wave speed, then the ship speed can not be changed from the wave speed, because the ship is in a state of statical equilibrium with regard to the ship speed. Since the critical condition is clarified as mentioned above, it becomes possible to estimate the critical wave height and ship speed for the surf-riding as a function of wavelength and wave direction for every type of ships and every loaded conditions, provided that the surge response function in following waves can be estimated exactly. A simple method for estimation of the critical wave height and ship speed is proposed and some examples of the chart of the critical curves for a stern trawler are also presented. The estimation of critical speed by means of the above method using Froude-Kriloff's hypothesis and neglecting the added mass, the resistance and the increase of the wave speed due to the dispersion by the finite wave amplitude, is in the safer side by about 10% than the experimental results. It is suggested that surf-riding is not always dangerous, and surge of large amplitude without surf-riding is not always safe. However the more difference exists between the ship speed in still water and the increased speed due to the wave motion which is equal to or close to the wave speed, the more dangerous situation is caused. The proposed simple method may be useful as a guide line for the safety of high speed crafts and other small ships like fishing boats running in the following seas from the view point of avoidance of the dangerous phenomenon of broaching-to.