It has been proposed that surface and interface stresses can modify the elastic behavior in nanomaterials such as nanowires. The authors show that surface stresses modify the tensile response of nanowires only when nonlinear elastic effects become important leading to cross terms between the applied stress and the surface stress. These effects are only significant when the radius of the nanowire is of the order of a few nanometers. The resulting alteration of tensile stiffness, though effected in part by the nonlinear elastic modulus, is particularly wrought by a modification of the stress state in the deformed nanowire.