Molecular dynamics and finite element simulations are performed to study the phenomenon of surface rippling in polymeric nanofibers under tension. Each nanofiber is modeled as a core shell system that resembles most relevant features extracted from detailed molecular simulations and experiments. Accordingly, our model nanofiber consists of a dense glassy core embedded in a less dense, more flexible, rubbery shell. Poisson's ratios of the core and shell layers are assumed close to that of compressible and incompressible materials, respectively. Surface rippling of the nanofiber is found, via combined finite element analysis and continuum theory, to be governed by a "polarization" mechanism at the core-shell interphase regime that is ultimately induced by the mismatch between Poisson's ratios while a mismatch between Young's moduli seems to play a secondary role. Plastic deformation is a prerequisite for the formation of rippled surfaces, that evolve from initial imperfections, and grow in the presence of uniaxial tension. For this reason, both strain rate and yield stress greatly influence the onset and modes of the observed rippled surface. Our findings are consistent with experimental observations on surface ripples of electrospun nanofibers and pave the way to design polymeric nanofibers with distinct surface morphologies.