Considering self-organized surface pattering upon multi-pulse femtosecond laser irradiation, in particularly the strong dependence of ripples orientation on the laser polarization, we present numerical simulations from an adopted surface erosion model and compare the result to our experimental data on laser-induced nanostructures formation. We present the surface morphologies obtained by this model for different polarizations of the incident laser electric field and show good agreement with ripple formation produced by laser ablation experiments. The correlation of ripples orientation with laser polarization can be described within a model where the polarization causes a breaking of symmetry at the surface. Further we discuss a time evolution of pattern formation. Our results support the non-linear self-organization mechanism of pattern formation on the surface of solids. (C) 2010 Elsevier B.V. All rights reserved.