In this paper a viscoelastic analysis of tape systems in winding/ unwinding process is presented. An analytical model is developed to predict stress and displacement fields in the tape system for any winding speed. A three‐parameter solid is used as an illustrated example. Results show that tape velocity is greater than 762 or less than 0.0762 cm/sec, the elastic solutions are applicaple. If the tape velocity is between 0.0762 and 762 cm/sec, the viscoelastic results are applicable.