The viscoelastic properties of vocal fold lamina propria tissue play an important role in tissue modeling, as well as in clinical studies of the effects of carcinoma, scarring, atrophy, or edema on dysphonia. Although the impact of these properties has been well studied, quantification of viscoelastic behaviors such as creep and stress‐relaxation continue to be important in the research. The current study examined the stress‐relaxation curves of ten canine vocal fold cover samples by stretching the tissue to 5%, 10%, 15%, and 20% of the sample reference length. The force on the lamina propria tissue was then recorded for 5 mins, and graphed so the stress‐relaxation response could be seen. The curves obtained were what we hypothesized, with the lamina propria tissue exhibiting exponential relaxation initially, and very slow decay at the end of the trial. These results are consistent with our previous studies on stress‐relaxation predicted by the biphasic theory of vocal fold tissue [Zhang et al., J. Acoust. Soc. Am. 123, 1627–1636 (2008)]. Finite element simulation has also been given to investigate the stress distributions within the vocal fold epithelium and lamina propria tissues.