A theoretical study is carried out to examine the influence of plate thickness on the stress state ahead of a through crack in a bent plate of infinite extent. The approach used rests on a theory in which no restrictions are placed on the mode of the stress distribution across the thickness of the plate. A knowledge of the local stresses or moments of the ensuing stress or moment intensity factor is held important in connection with modern views on the theory of crack propagation. The results show that the bending stresses local to the crack tip are drastically changed when the plate thickness increases from zero to some infinite, but small value. This is evidenced by the high elevation of the local moments as the ratio of plate thickness to crack length is perturbed slightly from zero.