PROBLEM TO BE SOLVED: To produce a transversely expandable/shrinkable composite sheet at a high speed by a simple production process while an elastomer is used effectively. SOLUTION: A nonwoven fabric 11 which is led to a fixed cylindrical support member 13 through a guide 12 is shaped cylindrically along the peripheral surface of the support member 13 and travels upward along the peripheral surface. Numbers of bobbins 15 are fitted to a turntable 14 rotating on the outside of the support member 13, and rubber strands 16 from the bobbins 15 are wound onto the nonwoven fabric 11 on the support member 13. In this way, a transverse arrangement body 17 in which the rubber strands 16 are arranged approximately in the transverse direction is formed on the nonwoven fabric 11 and joined to the nonwoven fabric 11 by a heating roll 18, so that the composite sheet 20 is produced.