The cuticles of many worms contain a cylindrical trellis made of layers of collagen fibres wound round the body in left- and right-hand helices. This kind of extensible skeletal structure imposes various constraints on a worm's behaviour, and some of these are examined, using the nematomorph Parachordodes woltersforffii as the main example. Upon extension or shortening of the cuticle, neighbouring fibres in one layer will eventually touch and so limit further movement; this in turn affects the extent of shortening, elongation, bending and coiling of the whole worm. Simple equations relate: the angle between a fibre and the worm's long axis; fibre spacing and radius; worm body radius and radius of curvature. The relevance to the life of the worm of fibre arrangement, matrix properties and volume changes is discussed.