A method for forming honeycomb structures by stepwise formation of channel walls reduces the pressure loading imposed by the extrudable material on a die that uses this method, facilitates the formation of well knitted channel walls, and requires only a minimum amount of lateral flow in the discharge zone to perform final interconnections between channel walls that have been substantially formed upstream of the discharge zone. The method presses extrudable material in substantially axial flow through a fist partitioning zone and subdivides the material into a series of flow segments having on their outer surfaces a portion of the channel wall surfaces formed. The extrudable material passes from the first partitioning zone in substantially axial flow while at least a portion of the channel walls formed in the first partitioning zone are maintained on the surface of the segments. Next, the extrudable material passes through one or more additional partitioning zones that again subdivide the feed material into additional flow segments by displacing at least a portion of the extrudable material from the axial flow path of the upstream flow segments, thereby forming additional portions of the channel walls on the surface of the segments. As the extrudable material continues to flow through subsequent partitioning zones, the portion of the channel walls formed in upstream partitioning zones are substantially maintained. The extrudable material passes through a discharge zone located downstream of the partitioning zones which causes the extrudable material to flow laterally and fill minor gaps in the channel walls that were left after passage of the extrudable material through the partitioning zones. An extruded honeycomb structure having a plurality of intersecting channels is recovered from the discharge zone. The method can be used with as few as two partitioning zones or as many as four or more partitioning zones.