Traditionally, fracture testing has focused on the fracture toughness of specimens undergoing pure mode I loading, often simplified by 2D assumptions of plane strain or plane stress. In reality, components have finite-thickness, and often see complex loading configurations. To study this complex behaviour, mixed-mode fracture specimens been developed. In this thesis, extensive three-dimensional finite element analysis is conducted to study two specimens: the (antisymmetric) four-point shear (FPS) specimen— a mode II test specimen, and the asymmetric four-point shear (AFPS) specimen — a mixed mode I/II specimen. Complete solutions of fracture mechanics parameters KI, KII, KIII, T11, and T33 have been obtained for a wide range of a/W and t/W geometry combinations. The thickness of specimen has a significant effect on the variations of both fracture parameter values and plastic zone sizes. The results presented here will be very useful for the toughness testing of materials under mixed-mode loading conditions.