Contact is one of the common positions for relationship existing between surfaces of mechanical components with line or point shape, which lead to different stress condition between them. Classic Hertz theory solved the stress distribution of two components with different contact form. The different stress form of contact components will result in different failure modes, and different strength requirement is needed in design. For those works under conditions like classic Hertz contact, obvious plastic deformation should be avoided and the maximum stress should be smaller than the allowed limit stress which is usually equal to yield stress of material. While for the ones enduring load by extrusion of two contact surface, the crushing of two contact surface should be avoided and the maximum contact stress should be smaller than the ultimate strength of the material. But for those works under varying stresses, fatigue and wear are common failure modes. The typical failure form resulted from contact fatigue is pitting and spalling; the previous one usually results in small peeling of materials from surface and lots of small shallow pits will formed, while the spalling usually leads to lager part of material drop off from the surface and scrap of mechanical components. Wear is another failure form of components works under contact conditions, which is actually can be seen as the accumulation of pitting of asperities. Comparing the classic static strength theory and fatigue strength theory of material, the static contact strength is actually the limit condition of contact fatigue strength with the one circle stress loaded in the whole life. With the development of fatigue theory, lots of models were proposed to study the contact strength of material from the fracture mechanics view. The most popular ones are critical plane method and Dang Van multi-axial fatigue criterion, which are used to assess the crack initiation of materials works under contact load.