The crack problem in a medium possessing coupled thermoelectric effect under thermal-electric loads is considered in this paper. The crack surfaces boundary conditions are assumed to be electrically and thermally impermeable. The general two dimensional solutions are presented in closed-form based on the complex variable method. Expressions for thermal flux, electric flux and stress fields in the vicinity of crack tip are derived. It is found that these fields exhibit traditional square-root singularity at the crack tip. For this, some essential fracture mechanics parameters, such as the thermal flux, electric flux and stress intensity factors at the crack tip are obtained. The results show that the electric flux intensity factor and thermal flux intensity factor depend on the far-field electric flux loads and the applied total energy flux loads, respectively. For the homogeneous isotropic thermoelectric material, only mode II stress intensity factor develops if the thermal-electric loads are applied.