Understanding the mechanisms governing temporal variability of ice stream flow remains one of the major barriers to developing accurate models of ice sheet dynamics and ice‒climate interactions. Here we analyze a simple model of ice stream hydrology coupled to ice flow dynamics and including drainage and basal cooling processes. Analytic and numerical results from this model indicate that there are two major modes of ice stream behavior: steady‒streaming and binge‒purge variability. The steady‒streaming mode arises from friction‒stabilized subglacial meltwater production, which may also activate and interact with subglacial drainage. The binge‒purge mode arises from a sufficiently cold environment sustaining successive cycles of thinning‒induced basal cooling and stagnation. Low prescribed temperature at the ice surface and weak geothermal heating typically lead to binge‒purge behavior, while warm ice surface temperature and strong geothermal heating will tend to produce steady‒streaming behavior. Model results indicate that modern Siple Coast ice streams reside in the binge‒purge parameter regime near a subcritical Hopf bifurcation to the steady‒streaming mode. Numerical experiments exhibit hysteresis in ice stream variability as the surface temperature is varied by several degrees. Our simple model simulates Heinrich event‒like variability in a hypothetical Hudson Strait ice stream including dynamically determined purge time scale, till freezing and basal cooling during the binge phase. These findings are an improvement on studies of both modern and paleo‒ice stream variability and provide a framework for interpreting complex ice flow models.