Cylindrical curved plates are widely used in structures such as aircraft skins and marine vessels. Corrosion significantly affects the structural stability of these curved plates. A finite element model was established to analyze the influence of corrosion on the post-buckling strength of curved plates. The reliability of the developed stochastic finite element model was preliminarily verified through comparison with theoretical calculations. Stochastic numerical analysis revealed the effects of parameters such as corrosion depth, corrosion location, and geometric dimensions on the stability and load-bearing capacity of the curved plates. The study found that the width (b)and height (a) had no effect on compressive load-bearing capacity, while mesh size, curvature radius (R), and diameter-to-thickness ratio (b/t) had significant impacts. The impact of corrosion depth (tc/t) was especially significant. This paper first proposed a theoretical formula to predict the reduction factor (η) for the compressive load-bearing capacity of uniformly corroded curved plates and then derived a formula for randomly corroded plates by modifying the equation for uniformly corroded plates. Finally, the study analyzed corrosion effects at different locations, revealing that the central region of the curved plate is the most sensitive to corrosion.