We elucidate the conditions under which an easy–to–catch edible prey species may evolve to resemble another edible species that is much more difficult to capture (‘evasive Batesian mimicry’), and the conditions under which two or more edible but hard–to–catch species evolve a common resemblance (‘evasive Müllerian mimicry’). Using two complementary mathematical models, we argue that both phenomena are logically possible but that several factors will limit the prevalence of these forms of mimicry in nature. Evasive Batesian mimicry is most likely to arise when it is costly in time or energy for the predator species to pursue evasive prey, when mimics are encountered less frequently than evasive models and where there are abundant alternative prey. Evasive Müllerian mimicry, by contrast, is most likely to arise when evasive prey species differ in abundance, predators are slow to learn to avoid evasive prey and evading capture is costly to the prey. Unequivocal evidence for evasive Batesian or Müllerian mimicry has not yet been demonstrated in the field, and we argue that more empirical work is needed to test whether putative examples are indeed a result of selection to signal difficulty of capture.