The existence of three-dimensional effects at cracks has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. Despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important. The purpose of the present investigation is to study by means of accurate 3D finite element (FE) models a coupled fracture mode generated by anti-plane loading of a straight through-the-thickness crack in linear elastic discs. The results obtained from the highly accurate finite element analyses have improved understanding of the behaviour of through cracked discs under anti-plane loading. The influence of plate bending is increasingly important as disc thickness decreases. Bazant and Estenssoro's analysis works well for the symmetric mode (mode I), but it is incomplete for the asymmetric mode (a combination of modes II and III). It appears that a new field parameter, probably a singularity, is needed to describe the stresses at the disc surfaces. Discussion on whether K-III tends to zero or infinity as a corner point is approached is futile because K-III is meaningless at a corner point. Calculation of the strain energy density (SED) in a control volume at the crack tip shows that the position of the maximum SED is a function of disc thickness