Abstract: For the cracked components under primary and secondary stresses, due to the different properties of primary and secondary stresses, the contribution of secondary stress to crack driving force varies with the range of plastic zone at the crack front, and the interaction between secondary stress and primary stress may lead to an increase in plastic deformation at the crack front or relaxation of plastic deformation at the crack front. Therefore, when conducting elastoplastic fracture mechanics analysis, it is necessary to correct the crack driving force caused by secondary stress, and the calculation method for correction coefficient and the factors affecting of the correction coefficient should be studied. This article firstly investigates the calculation method and physical significance of the correction coefficient V for the crack driving force induced by secondary stress, utilizing the reference stress method. Subsequently, it focuses on the engineering-common cylindrical structure with internal surface cracks. The finite element models with crack were developed for the structure with internal surface crack. The elastic and elastic-plastic fracture analysis were conducted under the independent and combined effects of primary and secondary stress loads, respectively. The crack driving force parameters were obtained, and the correction coefficient V of the crack driving force caused by secondary stress was calculated, and the influence of the primary and secondary stresses, as well as material properties, on the correction coefficient V was studied. The characteristics and differences of the calculation methods for correction coefficient V provided in the RSE-M and R6 code were compared. The methods in RSE-M and R6 code were used to analyze the crack driving force caused by secondary stress, and the calculation results were compared with those of the finite element method to demonstrate the applicability of the code method for calculating the crack driving force of cylindrical structures with cracks. The results indicate that the correction coefficient V is affected by primary stress, secondary stress, strain strengthening of material and interactions of those factors, which presents complex rules. The V decreases with the increase of primary and secondary stresses, exhibiting stress relaxation at the crack tip. The influence of the primary and secondary stresses on the V is more significant than that of material properties. The influence of material properties on the V is more complex and is influenced by the magnitude of primary and secondary stresses. The characteristics of the correction methods provided in RSE-M and R6 are different for crack driving force caused by secondary stress, and the correction results are more conservative than the finite element analysis results.