A composite elastic material 1 comprises a porous elastic carrier layer 3 to which is bonded a surface layer of a non-woven fabric 4. The composite material may be useful as a wound dressing, or as a component thereof. An impermeable film, hydrogel layer or adhesive layer may also cover the material. A blood-clotting agent may also be incorporated. Longitudinal L slits (7, see fig 3) may allow for transverse T expansion. The carrier layer 3 and non-woven layer 4 may be bonded by adhesive, stitching or welding 2, preferably welding using high-frequency or ultrasonic mechanical vibrations. A method of making such a material is also claimed, the method comprising feeding the layers between a sonotrode or sonic horn, and a pin-headed anvil such that the layers are bonded at multiple points 2 (see fig 4). The bonding may take place when the elastic is in a stretched configuration (see fig 2b), creating folds 5.