In order to solve the motion control problems of flexible squirming pipe robots and improve squirming efficiency in pipes, a flexible squirming pipe robot with structures of guide head and brake wheels is studied. A model of traction force is built through mechanics analysis of the robot in pipeline. In order to improve moving performance in different pipeline environments, the motion stability of the flexible shaft is analyzed, and the concept of the robot squirming motion instability is proposed. By using stability theory of cylinder, critical instability conditions of the flexible shaft in straight pipes and L-shaped pipes are derived, which provides theoretical basis for the robot's step planning. The pipeline experimental platform is built to accomplish experiments of traction force and moving. The test results are consistent with the theoretical analysis, which shows that the robot possesses outstanding traction ability, and the instability during moving process also verifies the correctness of the theory of flexible shaft critical instability.