A cylindrical structure composed of helicoidal transversely isotropic thick layers is considered. It models the behavior of structural elements with helically wound fibers. Such configuration is seen in yarns and cords, typically used as reinforcements in composite materials. Elasticity equations are derived for such a cylinder under axially symmetric loading. To account for the different behavior in tension and compression of the fibers, a bimodular elastic material is considered. The analytical results are compared with the finite element prediction.