Failure criteria for a crack between two dissimilar materials are presented. Test data from three different material pairs are considered. The first two consist of an interface crack between glass and epoxy and two dissimilar ceramic clays. For the third material pair, there is a delamination between two unidirectional carbon fiber polymer-reinforced plies with fibers in the 0 deg and 90 deg directions. Failure criteria for these materials have been presented previously. In this study, invariant parameters are used in the failure criteria. It is seen that the invariant length parameter has values which are unrealistically large and small. The preferred criterion is based on first principles.