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Fatigue and fracture of plate-like structures exhibit a strong dependence on thecross-sectional thickness, when the results are expressed in terms of stress-intensity factors. Atheoretical approach to account for this plate-thickness effect is presented, within theframework of the generalized plane-strain theory by Kane and Mindlin. Fundamental solutions(Green’s functions) for an edge dislocation in a plate of arbitrary thickness are first obtained,and then applied to analyze the effect of plate thickness on the elasto-plastic deformationbehavior at the tip of a through-the-thickness tensile crack.