It has been experimentally observed that wrinkles formed on the surface of electrospun polymer nanofibers when they are under uniaxial tension (Appl. Phys. Lett., 91, p. 151901 (2007)). Molecular dynamics (MD) simulations, finite element analyses (FEA), and continuum theory calculations have been performed to understand this interesting phenomenon. The surface wrinkles are found to be induced by the cylindrical core–shell microstructure of polymer nanofibers, especially the mismatch of Poisson's ratio between the core and shell layers. Through the MD simulations, the polymer nanofiber is found to be composed of a glassy core embedded into a rubbery shell. The Poisson's ratios of the core and shell layers are close to that of the compressible (0.2) and incompressible (0.5) polymers, respectively. The core is twice stiffer than the shell, due to its highly packed polymer chains and large entanglement density. Based on this observation, a FEA model has been built to study surface instability of the cylindrical core–shell soft solids under uniaxial tension. The “polarization” mechanism at the interphase between the core and shell layers, induced by the mismatch of their Poisson's ratios, is identified as the key element to drive the surface wrinkles during the instability analysis. Through postbuckling analysis, the plastic deformation is also found to play an important role in this process. Without the plastic deformation, the initial imperfection cannot lead to surface wrinkles. The FEA model shows that the yielding stress (or strain rate) can greatly affect the onset and modes of surface wrinkles, which are in good agreement with experimental observations on electrospun polymer nanofibers. The deformation mechanism and critical condition for the surface wrinkles are further clarified through a simplified continuum theory. This study provides a new way to understand and control the surface morphology of cylindrical core–shell materials.