Wireless communication of radio waves carrying orbital angular momentum (OAM) has been extensively studied in the past in a free space environment. In this paper, emphasis is put on the investigation of the interference due to a finite, electrically conducting plate on wireless communication based on OAM waves. First, the effect on the electromagnetic field distribution is demonstrated for varying sizes and locations of the conducting plate. Then, the effect on the wireless communication based on OAM waves in different modes is explored by using mixed-mode matrices. All investigations are based on the simulation of a circular array of electrically short dipoles using an adapted Method of Moments simulation tool. It is found in general that compared to the communication between two single dipoles, the effect of the conducting plate on OAM waves is similar but shows further dependencies. The obtained results imply that conducting surfaces in the vicinity of OAM based communication should be taken into consideration in the system design in realistic applications.