Based on the conventional Euler buckling model, uniaxial compression tests have been utilized recently to measure the mechanical properties of nanowires. However, owing to the increasing ratio of surface area to bulk at nanoscale, the influence of surface energy becomes prominent and should be taken into consideration. In this letter, an analytical relation is given for the critical force of axial buckling of a nanowire by accounting for both the effects of surface elasticity and residual surface tension. This study might be helpful to characterize the mechanical properties of nanowires or design nanobeam-based devices in a wide range of applications.