A simple superconducting loop with a Josephson junction subject to a time‐sinusoidal magnetic flux embedded in a noise background is considered. Cooperative effects, arising from the interplay between the noise and modulation are described; they manifest themselves in the response, measured as an output signal‐to‐noise ratio. In particular, it is shown that the response displays the stochastic resonance effect, wherein the output signal‐to‐noise ratio passes through a maximum at a critical value of the noise strength. A simple theory, based on the characterization of the superconducting quantum interference device as a bistable switching element, is seen to yield good qualitative agreement with the experimental results. ©1995 American Institute of Physics.