Effects of stress in passivation films on the electrical properties of (0001) AlGaN/GaN HEMTs are numerically analysed in the framework of the edge force model with anisotropical characteristics in elastic properties of group-III nitrides explicitly considered. Practical compressive stresses in passivation films induce negative piezoelectric charges below the gates and bring forth a-few-volt shallower threshold voltages. In addition, the shift in the threshold voltage due to the compressive stress is proportional to LG-1.1-1.5 with gate length LG, which is comparable to the expectation based on the charge balance scheme. These result suggest that passivation films with designed stress might play a crucial role in realising AlGaN/GaN HEMTs with shallow or positive threshold voltages.