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This paper studies the evolution mechanism of surface rippling in polymer nanofibers under axial stretching. This rippling phenomenon has been detected in as-electrospun polyacrylonitrile in recent single-fiber tension tests, and in electrospun polyimide nanofibers after imidization. We herein propose a one-dimensional nonlinear elastic model that takes into account the combined effect of surface tension and nonlinear elasticity during the rippling initiation and its evolution in compliant polymer nanofibers. The polymer nanofiber is modeled as an incompressible, isotropically hyperelastic Mooney-Rivlin solid. The fiber geometry prior to rippling is considered as a long circular cylinder. The governing equation of surface rippling is established through linear perturbation of the static equilibrium state of the nanofiber subjected to finite axial prestretching. The critical stretch and ripple wavelength are determined in terms of surface tension, elastic property, and fiber radius. Numerical examples are demonstrated to examine these dependencies. In addition, a critical fiber radius is determined, below which the polymer nanofibers are intrinsically unstable. The present model, therefore, is capable of predicting the rippling condition in compliant nanofibers, and can be further used as a continuum mechanics approach for the study of surface instability and nonlinear wave propagation in compliant fibers and wires at the nanoscale.