Purpose - The purpose of this paper is to numerically solve the problem of steady mixed convection boundary layer flow past a vertical flat plate embedded in a fluid-saturated porous medium filled by a nanofluid. The non-Darcy equation model along with the mathematical nanofluid model proposed by Tiwari and Das (2007) has been used. Design/methodology/approach - Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the nanoparticle volume fraction, the mixed convection and the non-Darcy parameters using the bvp4c function from Matlab. A stability analysis has been also performed. Findings - Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the opposing flow case (lambda<0). The stability analysis indicates that for the opposing flow case, the lower solution branch is unstable, while the upper solution branch is stable. In addition, it is shown that for a regular fluid (phi=0) a very good agreement exists between the present numerical results and those reported in the open literature. Research limitations/implications - The problem is formulated for three types of nanoparticles, namely, copper (Cu), alumina (Al2O3) and titania (TiO2). However, the paper present results here only for the Cu nanoparticles. The analysis reveals that the boundary layer separates from the plate. Beyond the turning point it is not possible to get the solution based on the boundary-layer approximations. To obtain further solutions, the full basic partial differential equations have to be solved. Practical implications - Nanofluids have many practical applications, for example, the production of nanostructured materials, engineering of complex fluids, for cleaning oil from surfaces due to their excellent wetting and spreading behavior, etc. Social implications - Nanofluids could be applied to almost any disease treatment techniques by reengineering the nanoparticle properties. Originality/value - The present results are original and new for the boundary-layer flow and heat transfer past a vertical flat plate embedded in a porous medium saturated by a nanofluid. Therefore, this study would be important for the researchers working in porous media in order to become familiar with the flow behavior and properties of such nanofluids.