Abstract: Based on the energy principles and the variational principle in finite deformation theory, considering the instantaneous configuration of crack, the paper establishes the incremental deformation caused by crack propagation, which can describe a more realistic mechanism for the expansion of the crack tip. The energy release rate and increase rate are proposed by taking the instantaneous configuration as the reference at the real physics state in the crack body. Also the crack propagation criterion is proposed. This propagation criterion describes the relationship between the energy and the crack growth per unit time per unit area of energy needed. It provides an approach for studying expansion of the crack tip.