The flux change &dgr; &Fgr; through a bistable superconducting quantum interference device has been measured in the presence of thermally induced switching (with rate &Ggr;) versus &dgr; &Fgr;x, the change in the applied flux. For small &dgr; &Fgr;x, &dgr; &Fgr; is proportional to &dgr; &Fgr;xwith a measured flux gaing, depending on the temperature, barrier height, and frequency &OHgr;, with a maximum of about 16. In agreement with theories of periodically driven stochastic bistable systems,g(&OHgr;) is nearly frequency independent up to &Ggr; and is proportional to &OHgr;−1for &OHgr;≫&Ggr;. For larger amplitude signals, harmonic generation has been measured in the adiabatic limit (&OHgr;≪&Ggr;) and found to be in good agreement with theory. Possible applications of this system for flux measurement are discussed. ©1995 American Institute of Physics.