The deployable composite cylindrical thin-walled hinges have important potentiality in the use of deployment mechanisms of satellite and solar array, but the progressive damage analysis of composite hinges hasn't been solved, which means the mechanical properties of the composite hinge are overestimated. The analytical and finite element models of composite tape springs are established, and the bending characteristics are analyzed. Theoretical and analytical solutions show good consistency. In addition, the progressive damage model of composite cylindrical thin-walled hinges is established and its folding and torsion characteristics are studied. The peak moment of folding is 4.41% reduced and the steady moment of folding is 16.22% reduced while taking progressive damage into consideration. In addition, the hinge has peak torsional moment of 18.48050 Nm and torsional angle of 15.37 degree correspond with Peak torsional moment.