A numerical procedure is described for predicting wave exciting forces and motions of multiple three-dimensional bodies of arbitrary shape freely floating in waves. The developed numerical approach is based on combination of a three-dimensional source distribution method and interaction theory which is exact within the context of linear potential theory. The method presented is applicable to an arbitrary number of three-dimentional bodies having any geometrical arrangement and individual body geometries. Numerical results of wave exciting forces and motions of two freely floating bodies in shallow water are compared with those obtained in the literature. The results of comparison confirmed the validity of the proposed approach. Finally, the interaction effects are examined in the case of an array of 40 (4 by 10) freely floating rectangular bodies in shallow water.