The influence of surface effects, including residual surface stress and surface elasticity, on the pull-in instability of electrostatic switches in nanoelectromechanical systems (NEMS) is studied using an Euler-Bernoulli beam model. This model is inherently nonlinear due to the driving electrostatic force and Casimir force which become dominant at the nanoscale. Since no exact solutions are available for the resulting nonlinear differential equation, He's homotopy perturbation method (HPM) is used to get the approximate analytical solutions to the static bending of NEMS switches, which are validated by numerical solutions of the finite difference method (FDM). The results demonstrate that surface effects play a significant role in the selection of basic design parameters of NEMS switches, such as static deflection, pull-in voltage and detachment length. Surface effects on low-voltage actuation windows are also characterized for these switches. The present study is envisaged to provide useful insights for the design of NEMS switches.