During oil and gas field development and production, the fault stability is very important. The fault instability may cause the casing damage and the leakage of oil and gas. In this paper, the coordinate transformation method is used to obtain the analytical solution on fault plane. Based on the comprehensive consideration of in-situ stress orientation, fault dip angle, fault strike and variation of in-situ stress, the influence of oilfield development and production process on the fault stability is analyzed using the analytical solution. It is found that the critical water injection pressure vary in different stress regime. Whether the reservoir pressure depletion can induce fault activity depends on the stress variation path coefficient. The smaller the coefficient is, the more stable the fault is, and the larger the coefficient is, the fault tends to slide with reservoir pressure depletion. At the same time, the study also found that the reservoir pressure depletion has a certain impact on the critical injection pressure. The greater the reservoir pressure depletion is, the lower the critical water injection pressure is.