A process is provided for producing extruded honeycomb bodies with passages, in particular as catalyst carrier bodies for the cleaning of exhaust gas from an internal combustion engine. The passages are bounded by wall regions which are at least partly provided with structures. The honeycomb body is extruded with an extrusion die in such a way that an additional relative movement between the honeycomb body and the extrusion die takes place, leading to a deformation of the wall regions of the passages. An extrusion die for producing extruded honeycomb bodies includes a multiplicity of secured profiled pins and a housing, which together form an extrusion mask. The extrusion mask is variable during the production process, so that wall regions with the structures can be formed. Honeycomb bodies which have structures in the interior that are suitable for influencing a stream of fluid flowing through can therefore be produced in a manner which is simple in terms of production engineering.