This work deals with the three-dimensional flow of nanofluid over an elastic sheet stretched non-linearly in two lateral directions. Suitable boundary conditions showing the power-law variation in the velocities are imposed. Further the recently suggested model for nanofluid is considered that requires nanoparticle volume fraction at the wall to be passively rather than actively controlled. A set of similarity transformations are introduced to convert the boundary layer equations into self-similar forms. The solutions have been obtained numerically through shooting method with fourth-fifth-order Runge-Kutta integration technique. The results reveal that penetration depths of temperature and nanoparticle volume fraction are decreasing functions of the power-law index. We notice that impact of Brownian motion in the temperature and heat transfer rate from the sheet is insignificant. (C) 2015 Elsevier Ltd. All rights reserved.