A beam is a slender member in which the bending moment and shear force are predominant. Members of skeletal frames, leaf springs, bridge decks, aeroplane wings, etc., are beams. This chapter deals with the stresses in thin beams due to bending and the deflection of its axis. An exact elasticity solution is derived for pure bending. Based on exact solution and equilibrium, shear stress due to shear force is obtained. Shear centre and solution for elastic perfectly plastic case and plastic collapse are discussed.