Low‐frequency noise in a hysteric rf superconducting quantum interference device (SQUID) originating from fluctuations of critical current of a weak link is considered. Such noise can be due to trapping‐detrapping processes within the tunnel barrier or to the presence of structural defects with internal degrees of freedom in the surrounding of the weak link. The defects can switch between two (or more) metastable states due to interaction with the thermal bath. On the other hand, elastic (and electric) fields created by defects act upon the critical current of the weak link inducing its fluctuations in time. Such noise is most important for high‐TcSQUIDs at high enough temperatures when defects are effectively interacting with the thermal bath. The dependencies of the intensity and statistics of flicker noise on the SQUID’s parameters and operating regime are analyzed. It is shown that higher correlation functions of output voltage at a given driving current can provide some information on the mechanism of 1/fnoise in rf SQUIDs.