The development of a numerical method for fissure formation during the carbonization of coke is needed because the formed fissures determine the coke's particle size. In this study, we proposed and developed a novel numerical method that can represent initiation, extension, and branching of multiple cracks. Fundamental tests (i.e., bending of a beam, stress analysis of a center crack plate, and crack propagation in a plate under tensile loading) were performed using the proposed method. The test results showed that the numerical accuracy of stress analysis and the fracture analysis using the proposed method were high and were comparable to other standard numerical methods. Furthermore, we applied the proposed method for the coupled analysis of heat conduction and thermal stress and performed numerical simulations for the formation of fissures in coke during carbonization. The numerical simulation results showed that major fissures extended in a linear direction, perpendicular to the direction of an oven wall. And the numerical results reflected qualitative features of an actual coke-making process using a chamber oven. Therefore, the proposed method could be used to reproduce the formation of fissures in coke during the carbonization process.