This paper developed a novel elongation type of Pneumatic Artificial Muscle (PAM), which is mainly composed of the expandable internal rubber tube surrounded by the external cylindrical helical spring and the two ends are closed. The PAM is not only the actuator of the flexible joint but also the core components to make up of the flexible joint. Therefore, the mechanical properties of the PAM directly influence the performance of the flexible joint. A mathematical model on the axial deformation and bending stiffness of elongation type of PAM was built applying theoretical analysis and experimental research methods. The results show that the axial deformation of PAM and the air pressure supplying to the PAM are nonlinearly related due to the generic nonlinear of deformation of the rubber tube; the bending angle of the PAM is proportional to moment; Similarly, the bending angle of the PAM is also proportional to its length. Furthermore, it indicates that the air pressure indirectly affects the bending stiffness of PAM as the air pressure directly influences the elongation of PAM. Finally, this paper provides a powerful framework for the dynamic analysis and motion accuracy control of the flexible joint or the robot which is composed by the artificial muscles.