A bandaging material in the form of a linear structure. The material has a first layer formed by a composite containing a thermoplastic polymer selected from the group of polymers and mixtures thereof, and a woody material derived from platy or granular wood particles having a minimum average size in one dimension of 0.1 mm. The material further has a second layer of a textile material having a first and a second surface. The first layer is superposed on the second layer in such a way that the first layer is essentially attached only to the first surface of said second layer. In this way, a bandaging material is obtained which has a suitably small self-adhesion which allows for it being coiled to a roll without force during manufacturing process. The bandaging material can further be uncoiled smoothly by hand followed by subsequent applying of it around limb at application temperature without delamination.