Soft, elastic materials are capable of large and reversible deformation, readily leading to various modes of instability that are often undesirable, but sometimes useful. For example, when a soft elastic material is compressed, its initially flat surface will suddenly form creases. While creases are commonly observed, and have been exploited to control chemical patterning, enzymatic activity, and adhesion of surfaces, the conditions for the formation and disappearance of creases have so far been poorly controlled. Here we show that a soft elastic bilayer can snap between the flat and creased states repeatedly, with hysteresis. The strains at which the creases form and disappear are highly reproducible, and are tunable over a large range, through variations in the level of pre-compression applied to the substrate and the relative thickness of the film. The introduction of bistable flat and creased states and hysteretic switching is an important step to enable applications of this type of instability.