Researches on the motions in waves have very important meanings for floating marine structures like offshore drilling rig, since they must be stationary platforms in the sea. The theoretical calculations of hydrodynamical forces upon such structures moving in waves are necessary for correct theoretical predictions of their motions. As a first step, in this paper is developed a method to calculate the wave forces acting upon groups of vertical circular cylinders, simple models of floating rig composed of several columns, fixed in waves with finite draft and infinite draft. This method takes into account the hydrodynamical interaction effect, which has ever been neglected, between cylinders due to the diffraction waves by each cylinder. Numerical results by this method, the wave forces on 2 or 3 cylinders, show that the interaction effect upon surging forces is not necessarily small especially in not large wave length range compared with the cylinder diameter. But in this wave length heaving force itself upon the structures is small and therefore the effect does not appeared clearly in this force. It must be investigated what an influence the effect has on their heaving or rolling motion in waves. The numerical results are in good agreement with measured ones obtained by comparatively simple experiment.