In this paper, an extremely accurate and efficient method for computing the interaction of a set of or multiple sets of general doubly periodic cracks has been presented on the basis of superposition principle, pseudo-traction method, and isolating analysis technique. A great number of typical examples are given in this paper. The stress intensity factors (SIF), the minimum strain energy density factors (SED) of crack tip and the critical stress (CRS) of crack growth are calculated with the accuracy of six significant digits for the rectangularly distributed periodic cracks and five significant digits for the general doubly periodic cracks. The relation of the interaction effect of the double periodic cracks with the periods and the ratio of crack length to crack spacing is analyzed. Also in this paper, the key technique problems for this method are discussed. (C) 2004 Elsevier Ltd. All rights reserved.