It is a challenging issue to fully consider the radiation interaction among floating bodies in a large array configuration. It requires large computational efforts to resolve the interaction matrix of floaters oscillating independently with 6 degrees of freedom (DoF). Obviously, when the distance between 2 floaters is large enough, their interaction will gradually vanish. It inspires the present study to investigate a cut-off radius, outside which the hydrodynamic interaction can be ignored. It should be noted that the computational efficiency and accuracy is a pair of contradictions: a large cut-off radius is always accompanied by a high accuracy, but requires more computational efforts, and vice versa. The objective of the present study is to quantify the interaction effect and to find an optimal cut-off radius which could reduce the computational time while ensuring a satisfactory accuracy in engineering practice. Based on the potential flow theory, we calculated the hydrodynamic interaction among multiple rectangular boxes and eventually quantified the interaction effects determined by the oscillating frequency and separating distance. Some critical curves of various truncation errors (Et) were obtained, showing whether the hydrodynamic interaction effects can be neglected, were depicted. The results from two case studies showed that the present cut-off scheme could provide a very reliable prediction of the hydrodynamic responses of multiple floating bodies in an array, while the computational time was significantly saved.