In this article, the deflection functions of nanobeams are found by employing the well-known Green’s function method. Based on Eringen’s nonlocal elasticity theory, stress gradient model is employed to formulate the problem. Different boundary conditions, including, clamped–clamped, clamped-free, sim- ply supported-simply supported and clamped-simply supported are studied. The beams are assumed to be under arbitrary distributed or concentrated loads. By presenting some new Green’s integral formula- tions, three different ways of treating the nonlocal terms are suggested. The specificity of inhomogeneous boundary conditions for the stress gradient nonlocal model is found. A particular property is a possible loss of the symmetry of Green’s functions for nonlocal boundary conditions. To validate the proposed results, findings are compared with the available ones in the literature.

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