The invention relates to a device for the treatment of free-form areas and zones of human or animal skin areas or plant surfaces by means of cold atmospheric-pressure plasma. The core of the device is a specific, preferably gas-permeable, electrode arrangement for generating a dielectrically impeded surface discharge where the earthed electrode is composed of electrically conductive textile material and the high-voltage electrode consists of a thin wire or electrically conductive thread which is sheathed with an insulting layer which has to meet specific requirements. On the basis of the present invention, it is possible to generate, in the area of diseased skin parts of the human body, in direct proximity to the skin surface or to wounds, a flat plasma for the treatment of the diseased areas which is acceptable in respect of the stress on the skin caused by temperature and electric potentials. The advantage of the gas-permeable textile sheet-like structure consists especially in that the arrangement can be placed flexibly onto variously curved surfaces and, in addition, offers the possibility of a gas exchange with the environment and/or the targeted dosing of a specific process gas mixture across the textile material into the active plasma zone.