A machine for forming a flexible paper drinking straw by forming annular corrugations in a tube includes a plurality of corrugating elements and means for moving the tube against the corrugating elements. Each of the corrugating elements is spaced apart from each other in both a lateral direction and a forward direction. The corrugating machine includes an assembly spool and a drum mounted to a side of the assembly spool for rotation about a common axis. A mandrel is mounted to the drum for reciprocation into and out of the spool assembly, to carry the tube against the corrugating elements mounted in an arc defined about the common axis.
