In this paper, we propose a new action planning approach to automatically pack long linear elastic objects into common-size boxes with a bimanual robotic system. For that, we developed a hybrid geometric model to handle large-scale occlusions combining an online vision-based method and an offline reference template. Then, a reference point generator is introduced to automatically plan the reference poses for the predesigned action primitives. Finally, an action planner integrates these components enabling the execution of high-level behaviors and the accomplishment of packing manipulation tasks. To validate the proposed approach, we conducted a detailed experimental study with multiple types and lengths of objects and packing boxes.