<p>To overcome the difficulties in assembly due to material deformation in non-rigid peg-in-hole tasks, this paper proposes a contact force-based multi-stage assembly strategy. This method divides the non-rigid peg-in-hole assembly task into the alignment stage, the initial insertion stage, and the adjustment insertion stage. In the alignment stage, a contact force model is established for the non-rigid shaft. By using a genetic algorithm to optimize the peg-hole angle deviation, the robot corrects the initial alignment errors and thus greatly reduces the computational demand of subsequent processes. In the initial insertion stage, the issue of frictional forces hindering the smooth sliding of the shaft in the non-rigid peg-in-hole task is addressed. A force control unit combined with a reinforcement learning algorithm is designed to achieve partial insertion of the non-rigid shaft when it is not yet in contact with the hole. In the adjustment insertion stage, a variable impedance controller is trained through reinforcement learning to insert the non-rigid shaft smoothly and precisely, achieving compliant control. Finally, experiments conducted under a tolerance of 0.00&#xa0;mm obtained a success rate of 100%, validating the effectiveness and robustness of the method proposed in this paper.</p>