To elevate the accuracy of the equations of motion of a ship advancing among the regular head seas, new equations have been developed for a slender ship by a modified method of slender-body theory. The coefficients of the equations contain three correction terms for the ordinary strip method which represent displacement effect, non-linear effect and three-dimensional effect, and can be calculated by making use of the well known velocity potential. Results of numerical analysis of 4212 W ship (series 60, C_B = 0.7) show that the three corrections improve qualitatively the common deffects which are found in most numerical results by the ordinary strip method but the amounts of correction are still quantitatively too large. Since there are possibly some other effects such as hull-shape nonlinearities in the experimental results, the authors wish to defer for a while the final conclusion on the accuracy of the ordinary strip method until such effects are clarified.