<p>Flexible objects exhibit deformability and high flexibility. Traditional strategies for manipulating rigid objects are often inapplicable, presenting a challenge for robot autonomy. This research aims to enable precise manipulation of flexible objects by robots, using a peg-in-hole (PiH) task as a case study. The focus of this paper is on the flexible slender peg made of soft material with high elasticity. Its unpredictable deformation under external forces makes traditional PiH strategies ineffective. Additionally, the deformation of a low-hardness flexible peg is difficult to detect with conventional wrist-mounted F/T sensors. Hence, we propose a tactile-based PiH strategy for flexible pegs (tactile-FPiH) that exhibits robustness to the material mechanical properties of different flexible objects. We employ a low-cost taxel-based tactile sensor capable of detecting the distribution of normal force. The deformation can cause a deflection of the peg in the gripper, leading to variations in the tactile signals. Leveraging this property, we design a specialized search strategy and develop a controller trained through reinforcement learning for alignment and insertion, while also implementing preventive measures to address potential peg-hole jamming issues. The results show that our approach can achieve a high task success rate with flexible pegs of three hardness levels.</p>