We demonstrate second and third harmonic generation from a GaAs substrate, well-bellow the absorption edge, in both transmission and reflection geometries. The pump is tuned at 1064 nm, in the transparency range, while the SH and the TH signals are tuned in the opaque spectral range of GaAs, at 532 nm and 355 nm, respectively. As expected, we find that the polarization of the generated signals is sensitive to the polarization of the pump. In our experiment, we work far from the phase matching conditions and we account for both surface and bulk contributions, and show that the surface-generated SH components can be more intense than bulk-generated SH signals. The experimental results are contrasted with numerical simulations that include these two factors, using a hydrodynamic model that accounts for all salient aspects of the dynamics, including surface- and bulk-generated harmonic components.