Abstract: To improve the operation stability and reliability, the effects of viscoelasticity for the tape spring on the strain energy, critical moment and steady moment exhibiting in the folding process were studied. The generalized Maxwell viscoelastic model was used to establish the mechanical model of the tape spring and numerical simulation was carried out to investigate the influence of different folding rates, temperatures, Prony series and relaxation times on critical moment, steady moment and strain energy in the bending process. Results show that the strain energy, critical moment and steady moment of the tape spring in the folding process cut down with decreasing folding rate, Prony series and relaxation time and increasing temperature. The strain energy and steady moment of the tape spring are reduced with the increase of the stowage time and gradually reach a constant value. This research has an important theoretical reference for improving the design reliability of space deployable structures.