The tension necking of FCC copper single crystal specimen with a square cross section was analyzed under the slip deformation mechanism. The actual clamp manner of the specimen was modeled by setting correlative boundary condition,and the small angle deflection between tension loading axis and crystallography axis [100] was taken into account. The finite deformation numerical analysis of three-dimensional necking deformation for the specimen was performed by applying crystal plasticity theory associated with a numerical algorithm suggested by the first author. According to the comparison with experimental observation, the fact was confirmed that the numerical results could describe the loading elongation curve of the copper single crystal specimen under large strain tension reasonably,and the method could be used to investigate the necking characteristic in neck shape and the effect due to the small angle deflection. Further, the investigation into the influence of specimen cross-section shape on necking was also performed;the results on mechanical response and neck profile evolution obtained through modeling of cylindrical specimen were compared with those obtained with square cross-section specimen.