A novel flexible pneumatic linear actuator is proposed in this paper. The proposed actuator realizes high-speed reciprocating motion by the moving part which has multiple rollers moves smoothly along the flexible hollow shaft. An effective application of this actuator is its use in endoscope robots and tether robots because cables of cameras or sensors can be passed inside the actuator by using the hollow structure. First, we discuss the physical model of the actuator pressurized in the resting state, and we provide an analysis of the generated force of the actuator. The model relates the generated force to the relevant design parameters such as the applied pressure, the material of the pressure chamber, the size of the moving part, etc. Second, we describe the measurement experiment of the generated force, and we show the validity of our model by comparing the experimental results with the analysis results. Third, we present the motion evaluation using a prototype of the actuator. We found that the maximum velocity of the moving parts is 9 m/s and that the moving parts can move smoothly even if the actuator is curved. Finally, we present the drive mechanism that uses the actuator, as an application example.