Abstract: In this paper, through analyzing the subcritical crack growth, a new formula is presented which can be used to calculate the crack fracture initiation stress at low and middle stress rates. By way of integration of the stress intensity factortime relation of crack under impact load, is attained a formnla from which the crack fracture initiation stress at middle and high stress rates cen be calculated. Combination of the two formulae leads to a general expression for caloulating the crack fracture initiation stress at all stress rate, low or high. The critical unstable fracture of material which contains many cracks is also analyzed in this paper, and a new viewpoint is put forward that the σfi-σ curve of material at high stress rate is an envelop of all σfi-σ curves of crack in the material, which leads to a conclusion that crack fracture initiation stress is proportional to the cube root of loading rate.