An exact theory is developed to evaluate propagation of an interfacial debonding in single fibre composite by means of the energy release rate due to crack growth. The debonding propagation during fragmentation test is significantly affected by frictional slip at the interface in the debonding region. Hence, frictional dissipation of the energy release rate occurs along with the debonding propagation. An analysis considering the effect of the interfacial friction is conducted. The fragmentation tests are performed varying the amount of fibre pre-stress, and the debonding growth is observed directly. To validate the present analysis, the debonding propagation predicted by the present theory is compared with the experimental one. The theoretical prediction is proved to be in the excellent agreement with the experimental results, which illustrates the importance of including the frictional effect in the energy release rate. An application of the present theory to fibre fragmentation in single-fibre composite test that can evaluate the fibre strength is described.