SUMMARY The purpose of this paper is to set up a new theoretical model of a fibrous structure in its filtering function. After the segmentation, using morphological transforms, of an image of a longitudinal cross‐section two models of penetration in the structure are proposed. They are developed from results of integral geometry like the Blaschke formula. These two approaches use different propagation laws: (1) gravitational transition; (2) turbulent flow transition. Finally, two sequences of coefficients are obtained characterizing a new vertical tortuosity law.