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Manipulation of deformable objects is a desired skill in making robots ubiquitous in manufacturing, service, healthcare, and security. Common deformable objects (e.g., wires, clothes, bed sheets, etc.) are significantly more difficult to model than rigid objects. In this research, we contribute to the model-based manipulation of linear flexible objects such as cables. We propose a 3D geometric model of the linear flexible object that is subject to gravity and a physical model with multiple links connected by revolute joints and identified model parameters. These models enable task automation in manipulating linear flexible objects both in simulation and real world. To bridge the gap between simulation and real world and build a close-to-reality simulation of flexible objects, we propose a new strategy called Simulation-to-Real-to-Simulation (Sim2Real2Sim). We demonstrate the feasibility of our approach by completing the Plug Task used in the 2015 DARPA Robotics Challenge Finals both in simulation and real world, which involves unplugging a power cable from one socket and plugging it into another. Numerical experiments are implemented to validate our approach.