I can not think of a single freshwater game fish that won't eat a crayfish. The biggest brown trout in Boulder Creek, both large and small mouth bass, northern pike, wiper and carp. Often an injured, or startled crayfish is the biggest and easiest meal a fish can get. Two great fly patterns are Dave Whitlock's "Near Nuff" and Patrick Knackendoffel's "Mud Slider".
Both of these flies are tied heavy and with weight properly adjusted to keep the hook point riding up. This allows the fly to be fished slow and on the bottom without snagging easily.