The mathematical model of mechanical behaviour of the fullerene C20 is constructed and realised in a package "Mathematica" at static loading in case of small deformations. Valency interaction the neighbour-them of atoms and molecular two more remote was considered. Consideration is spent within the limits of the theory of the central interaction and the valence-force-field theory. Estimations of the Young's modulus E of structure in a case when loading are made by axial and radial forces. At axial compression the Young's modulus is close to the modulus 20 – atoms nanotube (0.601 TPa). At radial loading 0.00540 TPa < E < 7.87 TPa (the scheme of the central forces), 0.00269 TPa < E < 3.93 TPa (the valence-force scheme).