The impact of chemical reaction and cross diffusion on heat and mass transport characteristics of viscoelastic flow of Al2O3 and CuO oil-based nanofluids past a porous nonlinear stretching surface has been examined. Similarity transformation was used to transform the governing partial differential equations into coupled nonlinear ordinary differential equations and solved numerically by employing the fourth order Runge-Kutta algorithm with a shooting method. Results for the entrenched parameters controlling the flow dynamics have been tabulated and illustrated graphically. The results foundCuO-oil based nanofluid to exhibit higher mass transfer rate and lower heat transfer rate and skin friction coefficient than Al2O3-oil based nanofluid under the same viscoelastic condition. This indicates that CuO-oil based nanofluid can be used as the working fluid in mechanical dampers.