We investigate here the stability of a gel cylinder subject to a strong surface tension. Both the criteria for the occurrence of a peristaltic instability and its dynamical evolution are determined within linear elasticity. Shrinking gels may show such an instability, as has been reported by Matsuo and Tanaka [Nature 358, 482 (1992)]. Considering approximate values of the relevant parameters, we find results in qualitative agreement with their experiments.