Based on the state of rock before failure in the working face of TBM, the double concentrated-force model is established for the working face under the thrust action of TBM disc cutters. Analytical expression of the stress distribution of rock under the coordinated action of double disc cutters is given by using the Boussinesq solution for the elastic half-space problem and the superposition principle. Based on the characteristics of stress distribution and the requirements for TBM rock breaking, necessary conditions for TBM rock breaking have been proposed, and the prediction formulas for the rock breaking thrust of disc cutter are provided using the uniaxial strength theory and the multi-axial strength theory, respectively. The engineering example shows that the rock breaking thrust of disc cutter predicted based on the multi-axial strength criterion proposed in this paper agrees well with the actual thrust during the TBM operation.