Abstract: This paper aims to study the torsional deformation of round rods with rough surface. The governing differential equation of round rod with rough surface are derived by the infinitesimal element method. The perturbation solutions of the torsion angle are obtained by combining perturbation method and discrete Fourier transform. The validity of perturbation solution in this paper is verified in comparison with the analytical solution and finite element solution of several round rods with typical rough surface. Systematic computations were conducted to explore the effect of statistical parameters on torsion angle and an empirical formula was established. The present work extends the solution range of torsion problem in Mechanics of Materials and provides a concrete mechanic example for methods of mathematical physics.