Apparatus for forming sheets of foamed synthetic plastics material, comprising a screw extruder, a nozzle head having an extrusion passage therein and a nozzle core positioned in the extrusion passage so as to form an annular nozzle, a cooled calibrating mandrel of a diameter larger than that of the annular nozzle, disposed downstream of the screw extruder having regard to the direction of extrusion and mounted on a stand, blowing means for applying internal pressure to an extruded tube between the annular nozzle and the calibrating mandrel to expand the extruded tube to the diameter of the calibrating mandrel, cutting apparatus for cutting open the increased-diameter cooled foamed plastics tube and apparatus for laying out flat the cut-open tube, wherein the nozzle core is rigidly connected to the stand of the calibrating mandrel and is connected to the inner wall of the extrusion passage by a single web aligned with the cutting apparatus whereby weakened and marked regions of the laid-flat cut-open tube are provided only at the extreme longitudinal edges thereof.