Fibrous zeolites (FZ) are the only group of natural zeolites that have been well investigated under pressure. The high-pressure (HP) behaviour of several FZ has been studied by means of in situ HP-single-crystal/powder diffraction experiments. Here I report a comparative study on lattice compressibility, structural deformation mechanisms and the role played by the framework (Si/Al-distribution, cross-linking of the building unit chains) and extra-framework content on the HP-behaviour of FZ. The structural analogy among the FZ group, due to the 4 = 1 secondary building unit (SBU), induces similar elastic behaviour and a “FZ-average bulk modulus” can be calculated: KT0 = 50±10 GPa. The bulk modulus value changes as function of the extra-framework content, following the sequence: KT0(Ba-FZ)>KT0(Ca-FZ)>KT0((Ca+Na)-FZ)>KT0(Na-FZ). Another interesting result is related to the axial compressibility. The experiments on natrolite, scolecite, edingtonite and thomsonite show that the elastic anisotropy, represented by the axial bulk moduli, is strongly influenced by the tetragonal topological symmetry. The HP-structural refinements performed show one main deformation mechanism for all these zeolites: the cooperative rotation (anti-rotation) of the SBU. This mechanism strongly reduces the free volume of the 8-membered ring channels, parallel to the SBU-chain direction.