To study the face stability of a shield tunnel drilling underneath an existing tunnel at close distance, a three-dimensional failure mechanism of the soil in front of the excavation face was constructed by using spatial discretization technology. Utilizing this failure mechanism and virtual work principle, the objective function of the chamber pressure for the shield machine under limit states was derived. The upper bound solution of the required chamber pressure for maintaining the stability of soil in front of the tunnel face during was obtained based on optimization calculations. Moreover, the influences of various parameters on both the chamber pressure and the failure modes of the front soil mass were investigated. Parametric analysis demonstrates that the required chamber pressure decreases with the shield machine approaches the existing tunnel and increases with it moves away from the existing tunnel. Applying the proposed theoretical methodology to the Guangzhou Metro Line 12 shield tunneling project, the theoretical solution of the chamber pressure were calculated. By comparing with the field-measured data of the chamber pressure, the validation of the proposed approach was proved.