Beam stiffness is an important concept for many types of structure, particularly those with slender shapes. Inadequate beam stiffness can lead to large deflections, and may also cause high localised stresses and a danger of failure in that region. In addition to bending moments, such structures may be subjected to twisting, or torsional moments (torques). In fact, virtually all structures, including buildings and many natural structures (trees, bones etc) are commonly subjected to significant applied moments. It is important to recognise the roles of structural shape, applied loads and material properties when predicting the resultant moments, deflections and stress distributions. The aim of this TLP is to provide the necessary information to allow such bending and torsional moments, deflections (both elastic and elastoplastic) and stress distributions to be predicted and understood.