<p>Thermoelectric materials have the characteristics of brittleness and low toughness and are prone to crack and hole defects in the process of preparation and operation. For the analysis of fracture mechanics, calculating and analyzing the stress intensity factor of hole-edge cracks is of great significance. On the basis of the complex function method, this study investigates the problem of a square hole with multiple cracks in a thermoelectric plate&#xa0;of infinite extent. By using the conformal mapping and the residue theorem, analytical expressions of the thermoelectric field and stress field can be derived. Then, the electric current density intensity factor, the energy flux intensity factor and the stress intensity factor at the tip of crack are derived based on the fracture mechanics theory. Comparison of the finite element method simulation results with analytical solutions can verify the accuracy of the analytical method. The results show that the intensity factors are proportional to the loads in the far field and have a tight correlation with geometric parameters of the defect. An increase in the semi-diagonal length of the square hole will increase the thermoelectric field intensity factor and the stress intensity factor. As the crack length grows, the thermoelectric field intensity factor decreases within a certain interval and then increases, while the stress intensity factor increases continuously.</p>