The ability to fold and deploy lightweight composites without damage makes them attractive for aerospace applications. However, one of the challenges faced with deployable composites is their high stiffness, which results in a relatively high deployment rate. It has been hypothesized that by exploiting the time-dependent viscoelastic response of composites, the deployment process could be controlled. To investigate this hypothesis, the effect of matrix viscoelasticity on energy dissipation of a three-layer carbon fiber–reinforced polymer (CFRP) composite laminate, known as a composite tape spring, was examined during the stowage state. A time-dependent implicit finite-element model was generated and implemented to simulate the viscoelastic behavior of the orthotropic laminated CFRP composite tape spring. The implemented material model was verified against data from the literature, validated experimentally, and then used to investigate the significance of matrix stress relaxation on energy dissipation of the three-layer CFRP composite tape spring used in aerospace applications.