A lightning arrester with a monolithic, active resistor core made of voltage-dependent resistance material based on ZnO is produced by mixing and grinding the base materials ZnO+metal oxides, producing pourable granules, filling into a silicone rubber tube and pressing cold-isostatically or radially into a moulding, sintering of the moulding into a self-supporting, monolithic resistor core, converting the resistor core, with an insulator by casting around, coating or painting with an epoxy resin, silicone material or concrete polymer or by drawing over a shrink-fit tube or by glazing. The resultant lightning arrester has a simple configuration, good reproducibility, cost-effective mass production.