A self‐consistent approach is proposed for the first time to describe the fracture in viscous plastic media taking into account the energy dissipation near the crack tip. The conditions are found under which slow heat‐ and stress‐stimulated crack propagation occurs. It is found that cracks of small size are unstable with respect to thermal and mechanical disturbances. It is shown that stick‐slip fracture instability due to the energy exchange between mechanical and thermal modes can take place at a certain stage of crack propagation. An estimation is obtained for the number of slips in the course of discontinuous fracture.