The paper dealt with material damping of fibrous composites for devices driven by artificial muscles as non-conventional driver. The composite material is intended mainly for rehabilitation devices, as well as for human artificial limbs, exoskeletons etc. The manipulator (rehabilitation) devices have potential to find usage in different periods of human life. Material properties of composites are suitable for applications with dynamic load, especially for their weight and material damping. On the base of experimental measuring, the material damping of several materials is analyzed.