In many industrial applications is necessary to predict fatigue lifetime of thin structures, where the stress field near the crack front have a real three-dimensional nature. Due to the existence of vertex singularity in the point where the crack front touching free surface, crack propagation in 3D structures cannot be reduced to a series of plane strain or plane stress problems along the crack front edge. The paper describes the influence of vertex singularity on the distribution of the stresses around the crack front for three-dimensional body. The distribution of the stress singularity through the thickness of the specimen gives us indication of the crack behavior in thin structures. The estimation of the thickness of the specimen where the change of singularity plays an important role on fatigue crack growth rate (in dependence on Poisson’s ratio) is carried out. The results contribute to a better understanding of the crack behavior in thin structures, and can help to more reliable estimates of their residual fatigue life.