Stokes’ first problem is studied to investigate the effects of nanofluid parameters on momentum, heat and mass transfers using the Buongiorno model. The experimental correlations for the properties of nanofluids are incorporated in the governing equations. A similarity analysis is performed to generate a set of ordinary differential equations describing the momentum, energy and mass transfers in the flow. These equations are solved numerically using the Runge–Kutta–Fehlberg method, which produces a fifth-order accurate solution. The numerical results are compared with the exact solutions for the regular fluids in the absence of nanofluid parameters and are found to be in good agreement. The results for the dimensionless velocity, temperature, wall shear stress, Nusselt and Sherwood numbers are presented graphically and compared for water-based nanofluids with ethylene-glycol-based nanofluids.