Abstract: The bifurcation of crack patterns is induced by crack-crack interactions. The interactions among cracks are studied by using pseudo-traction method. The bifurcation condition of crack growth patterns can be expressed by the crack length/spacing ratio. The crack-crack interaction will lead to the bifurcation of crack growth patterns if the crack length/spacing ratio is larger than the critical crack size/spacing ratio. The crack-crack interaction will not lead to the bifurcation of crack growth patterns if the crack length/ spacing ratio is smaller than the critical crack size/spacing ratio. Bifurcation conditions for arrays of two parallel cracks and arrays of infinite arrays of parallel cracks subjected to compressive stresses are analyzed from the theoretical point of view. The results are the closed-form theoretical solutions.