The tensile strength and compressive strength of most materials are different. The function of strength theory for these materials is expressed by two material parameters or two-parameter strength theory. This chapter illustrates the relationship of the Tresca criterion, the Huber-Mises criterion, the twin-shear criterion and other new criteria with the Yu-unified yield criterion. The three-dimensional stress state can be deduced to plane stress state if one of the three principal stresses equals zero. The materials having the identical tensile strength and compressive strength, such as mild steel, are widely used in engineering. The Tresca yield criterion and the Huber-Mises yield criterion are single-strength theories and are only suitable for certain kinds of materials.