The mechanics of an elastic helical coil are well known; however, the replacement of the elastic material with a viscoelastic material introduces a time dependency that requires a re-examination of the mechanics. A new theory has been developed that allows the prediction of the time to instability as a function of load, viscosity, and relaxation time, and is applied to an exemplar polyvinyl chloride (PVC) ring. The PVC ring shows that twist buckling dominates the instability, and the maximum critical time is approximately 90% of the relaxation period of the material achieved at a viscosity of 50%. Some viscosity is desirable to utilize the energy dissipation ability of a viscoelastic material. The new theory has a practical application in the field of nuclear reactor component design because the metals within the reactor are exposed to elevated temperatures thus exhibiting viscoelastic behavior. The Canadian Deuterium (CANDU®) reactor uses garter springs as spacers within the calandria of the reactor, and these spacers have been observed to move. A better understanding of the mechanics of the spacers may lead to improved spacer design.