In a tubular filter bodies with at least one tubular filter structure with a porous wall, through which a liquid passes substantially radially, particles above a given size being held back at the entrance surface, made of porous plastic, ceramic material, metal, graphite, etc, continuous operation at constant pressures is made possible by providing at least one groove (or slot) which is closed toward the outside and forms a forced flow path leading from an inlet to an outlet in the circumferential entrance surface of the tubular filter body.