In this article, three dimensional elastic-plastic curved crack tip opening displacement under quasi-static loads has been mainly studied, and three dimensional curved crack tip opening displacement has been calculated as a practical application of a second order perturbation method, where the effects of quasi-static applied stresses and quasi-static normal and shear stresses on the boundaries of plasticity area are synthetically taken into considerations. Three dimensional curved elastic-plastic crack tip opening displacement has been calculated by numerical solutions, diagrams have been constructed to analyse the transformation relationships between curved crack tip opening displacement and three dimensional crack body geometrical measurement. Curved crack tip opening displacement will decrease when three dimensional crack body thickness increases. When crack body thickness increases evenly, three dimensional curved crack tip opening displacement will continuously decrease, furthermore, the decrease extent will be more and more slightly, and tend to plane strain state ultimately. Curved crack tip opening displacement will increase when external loads increase with the same crack body thickness. A new theoretical model where curved crack tip opening displacement was calculated has been established in three dimensional crack body.