The author treated the problem of torsion of a prismatic cylinder by deriving a torsional stress function : - [numerical formula] The cylinder has the hyperbolic bow section whose boundary is composed of a straight line and a kind of hyperbolic curve. Experiments have been done on the test pieces with hyperbolic bow section and also with circular-arc bow section. The above stress function derived can approximately be applied to the test pieces with circular-arc bow sections with small thickness.