A process for the elimination of heavy metals, in particular mercury and possibly arsenic and lead, present in a gaseous or liquid effluent by means of a fixed bed process using an adsorbent in the form of monolithic or supported extrudates, said extrudates being characterized by a length h and a section comprising at least three lobes. The adsorbent is composed of at least one active phase based on sulphur in the elemental form or in the form of a metallic sulphide. The process is advantageously applicable to the treatment of gas of industrial origin, synthesis gas, natural gas, gas phase condensates and liquid hydrocarbon feeds.