A model is suggested for calculating the mechanical characteristics of sintered highly porous fibrous materials (HFM) (porosity 90%) in which the measured characteristics of the microstructure of the material are used as initial parameters: mean length and diameter of fibers, anisotropy of fiber arrangement, size of contact bridge, also mean mechanical characteristics of the fibers. It was assumed that fibers arranged along the direction of expansion has a finite length and are loaded by the bending of transverse fibers in contact with them which fulfill the role of a matrix (transfer of shear stresses). The concept is introduced of a value for the contact bridge (CB) between the fibers of the HFM.