Optical interconnections are promising optical computing. It will take place of conventional electronic interconnections in many areas. Backplane optical interconnections between boards are studied at present. Beam spot shift mainly influences on quality of backplane optical interconnections between boards are presented. The causes are analyzed and first order approximate formulas of relation between locations in the interconnections and slant degrees between two planes of light guiding plate in the interconnections are deduced by using first order approximation in this paper. According to laboratory deviations, different kind of deviation result and the total deviation result of interconnections are estimated. The method of overcoming beam spot shift in backplane optical interconnections is proposed. In the laboratory, high quality elements of backplane optical interconnections between boards are fabricated and it proves that the deduced approximate formulas in this paper are right. These will help to realize applications of backplane optical interconnections between boards.