Some concrete analyses were performed using ANSYS software for analyzing the edge stress field of the contact field and the stress intensity factors when a rigid indenter and an elastic half-plane was contacted taking an elastic halt-plane of carbon steel as example.The result shows that the contact stress field was symmetrically distributive,and the contact stress rapidly reached a maximum value at the edge,there was an evident stress concentration phenomenon,and different loads,material properties,geometric shapes had different influences on the stress intensity factors.The stress intensity factors in the contact field under various working conditions can be derived under the condition without a theoretical value based on the mentioned above.