In this study, theoretical bi-elastic constant α for an interface crack between dissimilar anisotropic composite materials has been obtained. The obtained theoretical solution has been settled to the equation which defines conventional α for an interface crack between isotropic materials, when it brings each material property close to the characteristic of isotropic composite ones. The remarkable conclusion is to determine α regardless of the direction of the boundary surface, if angle difference between anisotropic strongest axes in both sides is fixed.