A flexible fiber bundle shape sensor with a thin diameter and its glue injection packaging device are designed. By the distributed strain measuring technology of an optical frequency-domain reflectometer, we experimentally explore the influence of the glue material and ratio on the generation, accumulation, and distribution of residual stress in the packaging process of the sensor. The experimental results reveal that the cross-linking reaction of glue makes the residual strain gradually increase with the curing time. Moreover, for the three optical fibers in the shape sensor, the accumulation of residual strain with time and the spatial distribution of residual strain along the fiber axle are consistent. After about 16 h curing reaction, the residual strain of the three fibers reaches the maximum and remains stable in the range of 80-100 με. The research results minimize the residual strain during the packaging process of the optical fiber shape sensor and lay a foundation for high-precision shape measurement.