This paper presents a result of theoretical calculation on the resistance law of an arbitrary type of roughness. Rough surface is classified into two types in the high speed range according to fluid dynamical properties. One is the sand roughness and the other wavy roughness. However, to find the general characteristics of arbitrary type of roughness is practically impossible and it is necessary to carry out the model test to know the fluid dynamical property of the particular roughness. In order to find the method of extrapolation from the model data to the ship, it is important to know the resistance law of roughness, especially the charateristics of the line Uk / v = constant, where k is the height of the roughness. For this purpose, a calculation was made on the the basis of momentum integral method considering the effect of velocity defect due to roughness. The following simple formula was found to exist between the increase of resistance coefficient of the model Δ C_fm , and of the ship Δ C_fs . Δ C_fm /Δ C_fs = (Δ C_fm /Δ C_fs ) ² with Uk /ν=constant, where C_fm and C_fs are the frictional resistance coefficients of the model and the ship, respectively.