This paper shows a fundamental investigation concerning a non-uniform theory of wave resistance. The author applied to the theory the new method that he analysed in his other paper¹⁾ in the conception of acceleration potential. In this paper the author analysed a non-uniform fluid field. of surface wave that is caused by a ship moving with constant velocity describing harmonic oscillations and treated only two dimensional case, but it will be also developed in three dimensional case by the same process. The subject of this paper is a deduction of a velocity potential and an integral equation that determines a relation between motion of a ship and fluid pressure on the ship.