In this paper, the interaction of double-periodical cracks is accurately solved based on the isolating analysis procedure, superposition principle, pseudo-traction method, Chebyshev polynomial expansion and crack-surface collocation technique. The jump displacement crossing crack faces, the average additional strain and therefore the effective compliance of the double-periodically cracked plate are directly determined. The numerical results for axial-symmetrically distributed double-periodical cracks, general double-periodical cracks with one collinear direction as well as two sets of double-periodical cracks with same size and square distribution are given in this paper. And the partial typical numerical results are compared with the previous works. The analysis shows that the anisotropy induced by the general double-periodical cracks is generally not orthogonal anisotropy. Only when the double-periodical cracks are axial-symmetrically distributed, is the anisotropy orthogonal. In this special cases, the effective engineering constants (consist of effective elastic modulus, the effective Poisson's ratio, the effective shear modulus) of cracked plate versus crack spacing, in the plane stress and plane strain conditions, respectively, are analysed. Copyright (c) 2005 John Wiley & Sons, Ltd.