Due to their tailored thermomechanical behavior and functionality, shape memory polymer matrix composites (SMPCs) are attractive as deployable structures in aerospace applications. An analytical model based on the classical laminate theory, together with the principle of minimum potential energy is developed to capture the thermo- viscoelastic behavior of a bistable tape spring (BiTS). These tape springs are known to snap between two stable configurations by different stimulus. Here, a shape memory polymer as the matrix of a fiber-reinforced polymer BiTS is introduced to actuate the snap-back. Experimental characterization was performed to obtain the time-temperature dependent properties of a Polyurethane SMPC. The time-temperature superposition principle was employed to convert the thermal effects to a viscoelastic response. Five BiTSs were manufactured and exposed to two different thermo-viscoelastic cycles to verify the model for long-term and high-temperature behaviors. The results show that the model can estimate the coiling radius and the degree of stability of the BiTS in the coiled configuration. Analytical results, supported by experimental results, show that the temperature could initiate the snap-back in BiTS. However, time-temperature history has a significant effect on the bistability and can convert a monostable tape spring to a BiTS and vice versa.