A microscopic calculation of the anisotropic nonlinear optical surface response of Al(111) is performed within the nearly free electron approximation. The bulk potential is described in terms of the most important Fourier components of the lattice potential and the self-consistent Lang-Kohn potential is used as surface barrier. The dynamical response is treated within the independent particle approximation. The anisotropic tangential surface current is shown to exhibit a surprisingly large penetration depth that is determined by the spatial inhomogeneity of the electronic states near the band gaps. The frequency dependence of the anisotropic surface polarizability element X xxx ( ω) exhibits resonant behavior at ω or 2 ω near 1.5 eV, i.e. close to the onset of the main interband transitions caused by V 200. The magnitude of the anisotropic surface polarizability is comparable to that of the main isotropic component. These results are in qualitative agreement with the available experimental data on Al(111). It is argued that the large penetration depth of the tangential surface current does not imply a weak surface sensitivity of X xxx since this current should be sensitive to the electron scattering conditions at the surface.