A constant volume flexible joint system includes a flexible membrane for coupling across a joint and spaced radial support ribs fitted to the membrane. Axial support structures are coupled to the spaced radial support ribs preventing axial deformation of the joint due to a differential pressure. The axial support structure preferably include pivoting sockets and blocks enabling the joint to flex and the flexible membrane to contract on the inside of a bend and expand by an equal or near equal amount on the outside of the bend resulting in a constant volume joint that requires low or no torque throughout the bending motion.