A refinement of the previously constructed models of bending of the Timoshenkoand Euler–Bernoulli nano-rod with taking into account the Steigmann–Ogdensurface elasticity is considered. This refinement increases the coefficient of thelower derivative of the deflection in the bending equation by 50%, which cansignificantly affect the size effect. Updated results of modeling of buckling of a simply supported nano-rod and a nano-cantilever under its own weight.