A capsule-type soft pneumatic actuator (CTSPA) was molded with hyperelastic material (latex) and subjected to deformations. In order to provide a large thrust force and limit the direction of expansion and contraction, the actuator was covered by fiber materials and driven by compressed air. Soft pneumatic actuator, belonging to flexible drive, showed nonlinear characteristics. In this study, with theoretical and experimental methods, a static mathematical model of CTSPA was established to analyze the relationship between the inflation pressure, driving force, and deformations. Furthermore, we experimentally explored the response characteristics of CTSPA by using a unit step function. The hysteresis was significantly affected by air pressure, loading size, and effective contact area of the actuator. Finally, the actuator realized a compatible position tracking performance of 1 Hz and a low average tracking error of 0.3°. The study provides a basis for studying the control methods and state maintenance of flexible drive systems.