Soft pneumatic actuators (SPAs) that can twist dominantly provide a promising solution for the design of soft robots due to their flexibility, compliance, and easy fabrication. However, the torsional SPAs also face challenges such as overpressure risk and small torsion angle. To tackle those challenges, a new type of torsional SPAs is designed based on the reversible, cooperative buckling of elastomer, which yields a torsion angle of 1.94 deg/mm and an output torque of 26 N .mm with a secure operation pressure. Moreover, this actuator can achieve a wide range of torsional motion by varying the structure parameters, including the height of actuators and the pitch of helical chambers. The relationship between structure parameters and actuator performance is investigated experimentally, and experimental results show that the torsion angle and output torque increase with the height growing from 20 to 44 mm, while decrease with the pitch rising from 75 to 150 mm. The effect of different materials used for constructing the actuator is also studied numerically, and results show that the output torque can be improved by changing the materials. Additionally, several soft machines constructed by utilizing the actuators as a torsional joint are able to perform different manipulating tasks, such as screwing the light bulb, grasping and rotating objects. The actuator developed in this paper is capable of extending the researches on SPAs and offering an alternative for the actuation of soft machines.