An arrester for lightning protection of electrical equipment or power transmission lines is disclosed. The arrester comprises an insulating body made of a dielectric and five or more electrodes mechanically connected to the insulating body and arranged to allow the formation of an electric discharge between adjacent electrodes under the influence of lightning overvoltage. The electrodes are located inside the insulating body and separated from its surface by a layer of insulation. Adjacent electrodes exit into discharge chambers having outlets to the surface of the insulating body. At least a part of the discharge chambers is provided with pressurizing chambers located near the electrodes and connected to the discharge chambers through the discharge gaps between adjacent electrodes. Thanks to the invention, the discharge arc is extinguished after the passage of the lightning overvoltage pulse before the follow current having the industrial frequency passes through zero, mainly immediately after the lightning overvoltage pulse.