One of the challenges facing the designers of aeroengine drive shafts is to transmit higher torques while at the same time reducing the overall diameter of the engine in order to reduce drag. The resulting high performance drive shafts are smaller, lighter and have thinner walls and it is essential that the factors affecting instability are known and understood. Torque is the principal load carried by these shafts and most of the analytical methods for predicting torsional stability are either analytical or semi-empirical and tend not to cover the relevant range of geometries of interest here in terms of shaft geometry. Also, they give only limited information about the failure mode involved. A finite element analysis (FEA) approach has been developed to address this need and this paper presents results for plain shaft sections subjected to torque loading. Geometries leading to elastic buckling and plastic collapse are identified, along with appropriate formulae for calculating the torque capacity.