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Surface effect on the longitudinal and flexural wave propagation in straight nanofibers/nanowires is studied within the framework of continuum mechanics. Modified Euler-Bernoulli and Rayleigh-Love rod equations and modified Timoshenko beam equation were developed to take into account the surface effect. It was found that surface tension/stress plays appreciable influence on the wave propagation in nanofibers/nanowires at very small diameters. Wave dispersion relations were presented in closed form, and numerical calculations were performed to show the variation of the phase velocity with the wave number at varying surface property and fiber diameter. The given results can be used as the theoretical basis of dynamic characterization of nanofibers/nanowires and nanodevice design and analysis.