We report a model of nanowire (NW) mechanics that describes force vs displacement curves over the entire elastic range for diverse wire systems. Due to the clamped-wire measurement configuration, the force response in the linear elastic regime can be linear or nonlinear, depending on the system and the wire displacement. For Au NWs the response is essentially linear since yielding occurs prior to the onset of the inherent nonlinearity, while for Si NWs the force response is highly nonlinear, followed by brittle fracture. Since the method describes the entire range of elastic deformation, it unequivocally identifies the yield points in both of these materials.