In this paper, out-of-plane static behavior of circular nanobeams with point loads is investigated. Inclusion of small length scales such as lattice spacing between atoms, surface properties, grain size etc. are considered in the analysis by employing Eringen's nonlocal elasticity theory in the formulations. The nonlocal equations are arranged in cylindrical coordinates and applied to the beam theory. The effect of shear deformation is considered. The governing differential equations are solved exactly by using the initial value method. The displacements, rotation angle about the normal and tangential axes and the force resultants are established and the analytical expressions are presented. The predicted trends of the size effect at the nano scale agree with those given in the experiments. The results can be used for designing nanoelectromechanical systems (NEMS) where the curved nanobeams are used as a basic component. (C) 2016 Elsevier Ltd. All rights reserved.