A fibre is an elongated object: compressed along its axis, it can bend suddenly, an instability known as buckling. Intriguingly, a collection of fibres can also become unstable when compressed: they form a crease. Creases are well-known in soft incompressible materials like natural tissues or elastomers – but why do they form in such an apparently different system? To answer the question, we need to understand how fibre assemblies deform. Collaboration : Saint-Gobain Research Paris (Aubervilliers) - Rensselaer Polytechnic Institute (Troy, NY, USA).