In the present paper, a fractal model of a porous layer formation is proposed. The consideration of the time-dependent pore growth process has allowed us to calculate such important parameters of porous matrix as the formed surface area, and surface and volume porosity values. We have theoretically shown that the formed surface area strongly depends on the difference between the pore size growth velocities parallel and perpendicular to the surface, i.e. the crystallographic orientation of the material surface. The volume and surface porosity values as well as the formed porous surface area are linear functions on the anodization current density. These results are in rather good agreement with other theoretical and experimental data.