Stress corrosion crack (SCC) of small crack has an important effect on the whole-life attenuation process of critical structures in nuclear power plants (NPPs). By combining the film slip-dissolution/oxidation model with the elastic-plastic finite element method (EPFEM), the quantitatively predicting of SCC propagation rate for small crack in reactor pressure vessels (RPVs) of NPPs. According to the crack tip mechanical field analysis, the crack tip strain rate is determined to control the initiation and propagation of small cracks, and it is approximately calculated by the variation of plastic strain (de_p/da) at a characteristic distance r₀ in front of a growing small crack tip. Two methods of dynamic crack propagation method and quasi-static crack propagation method based on EPFEM were proposed to calculate the variation of plastic strain (de_p/da). The contrast of the two calculation method and the sensitivity analysis of variation of plastic strain to the crack length were carried out, which concludes that the slight differences between the two methods, and the plastic strain variation are more sensitive to crack propagation with small crack than that of long crack. The SCC propagation rate of small cracks is larger than that of long cracks, and it is significantly influenced by the characteristic distance r₀. As it is difficult to determine the value of characteristic distance r₀ finally due to the unclear of its meaning, it is suggested to be determined by combining experimental SCC data with a finite element simulation of the single-edge crack panel specimens under the same environmental and material conditions. The approach proposed in this paper is expected to quantitatively predict SCC propagation rate in core materials and evaluating SCC propagation in key structural components in NPPs.