Although the problem of the stability of a fuselage that is subjected to torsional force is important in connection with the case of light metal construction of an aeroplane in flight, the theoretical side of the problem does not seem to have received much attention. This is probably because of the difficulty of obtaining its mathematical solution even in the case where the fuselage is assumed to be a circular hollow cylinder. Thus, I studied the problem in assuming that the fuselage is a cylindrical shell for the first approximation. Southwell and Skan have dealt with the stability of a plane elastic strip due to edge shearing forces, but their result cannot be applied to the problem of the cylindrical shell unless its length is very short. Schwerin seems to be the only one who has written on the torsional stability of a cylindrical shell. Although his method of constructing the differential equations of the equilibrium of a cylindrical shell has been chiefly derived from Love's text book, and appears correct in the main, yet owing to the certain apparent particularities on his part his solutions of equations are open to grave doubts.