Cataloged from PDF version of article. Thesis (M.S.): Bilkent University, Department of Mechanical Engineering, İhsan Doğramacı Bilkent University, 2019. Includes bibliographical references (leaves 77-80). Interest in nanobeams is increasing as their application areas widen and new properties are discovered. These structures exhibit size dependent intrinsic properties that are absent in macroscale. This requires employment of new material models as bulk models by themself are not sufficient to describe the physics unless one considers the domain as a composite material, which is undesirable. In this work it was confirmed that incorporation of surface elasticity results in a good match with experiments. Moreover it was shown that due to lack of out-of-plane shear support of surfaces and curves, Euler beam assumptions fail for numerical implementations when the beam size reduces. This phenomenon was shown to be a severe drawback for curved energetic domains with a still noticable effect for surface energies. A geometrically nonlinear buckling model is proposed based on linear elastic material model. It is implemented in an ordinary differential equations solver and the solutions were confirmed to meet the finite element method (FEM) results to a very high degree. The theory is integrated with surface layers in which its accuracy was confirmed when compared with FEM results. by Onur Vardar M.S.