Factors such as processing techniques, daily abrasion, and atmospheric corrosion lead to a specific level of surface roughness in component surfaces. This paper examines the tensile and compressive deformation behavior of circular rods with axisymmetric random rough surfaces. First, a digital reconstruction of the rough circular rod model was conducted, where the rough surface was jointly characterized by two statistical parameters: root mean square height and correlation length. Then, the dimensionless governing differential equation for both tensile and compressive cases of the rough circular rod was derived through the infinitesimal element method. Subsequently, in combination with the perturbation method and the fast Fourier transform, the governing equation was solved, yielding the perturbation solutions for both types of deformation of the rough circular rod. The validity of these solutions was verified through comparisons with analytical and finite element solutions. Finally, to explore the influence of the statistical parameters of rough surfaces on tensile and compressive deformation, the contributions of first-order and second-order perturbation solutions were systematically compared, and an empirical formula for the perturbation amplitude was established. The effect of perturbation on the results gradually increased with root mean square height and correlation length; the proportion of the second-order perturbation solution rose with root mean square height but remained unaffected by correlation length. This work not only expands the research scope of traditional problems in mechanics of materials related to tensile and compressive deformation, but also provides an example of the application of mathematical and physical methods in mechanical practice. Moreover, this study offers a theoretical basis for optimizing the manufacturing processes of components and quantitatively assessing the impact of surface defects on the mechanical properties of components.