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A finite element alternating procedure developed to deal with the cracked plate in symmetric bending is extended to analyse the more realistic case with single or multiple mixed mode cracks. This modified procedure involves the new derivation of the analytical solution for an infinite thin plate containing a crack subjected to arbitrary anti-symmetric equivalent shear force on crack surfaces. Due to the natural limitation of Kirchhoff assumptions for a thin plate in bending, the appropriate treatment of constant twisting moments on the crack surfaces is devised. The interaction effect among cracks on the calculation of bending (symmetric) and shear (anti-symmetric) stress intensity factors is also discussed. Several numerical examples are solved to demonstrate the validity and efficiency of the approach.