Abstract: Stress intensity factor is one of the most important parameters in fracture mechanics. Based on the principle of virtual work and bending theory, this paper proposes a method to estimate the stress intensity factor for circumferential cracked elliptical pipes by adopting the energy release rate of “non-spontaneous” crack extension, i.e., G^*-integral theory, and derive the expression of the stress intensity factor for circumferential cracked elliptical pipes under different loads. The comparison between the proposed method and finite element method shows that proposed method can give an analytical solution and is simple in calculation.