An undercritical drive shaft and a method of producing the undercritical drive shaft from fiber composite material is disclosed. The drive shaft, which is produced of fiber composite material and is to be used as an undercritically operating shaft, has a high damage tolerance with respect to resistance to torsion and the manufacturing process requires lower expenditures. For the drive shaft, the fiber composite material consists of several successively individually wound-up webs of prepreg. For the method of producing the drive shaft from fiber composite material, as the fiber material, the web-shaped prepreg is wound onto the winding spindle and this prepreg is deaerated and simultaneously compressed by the winding-on of a thermoplastic woven band which is prestressed in a defined manner. The thermoplastic woven band is unwound again and additional prepreg layers are then wound up which are then deaerated and compressed in the same manner by a thermoplastic woven band.