Composite beams of carbon fibre reinforced polymers (CFRP) and steel, formed as tubular steel sections externally reinforced by CFRP sheets, have characteristics of structural and economic advantages. Such structures exploit the best attributes of both composite fibres and steel, resulting in greater strength and ductility to circular hollow steel (CHS) sections without increasing the section size. The governing failure mechanism of a hollow steel beam often concerns the premature local buckling of the steel wall that is attributable to the thin-walled nature of the section. The potential identification of CFRP reinforcement incorporated into steel CHS beams has not been adequately achieved in particular in pure moment regions. This paper provides an experimental study consisting of hollow circular steel beams reinforced by thin carbon fibre sheets and subjected to pure bending. The role of the composite reinforcement is to interact with the enveloped tube section and to restrain the tube to deform in a favourable fashion for strength enhancement. The tests reveal that the bending strength of CHS steel beams increases with different circumferential reinforcing orientations. Accompanying these experiments is the assessment of a theoretical method which employs the modular ratio concept and considers the AS 4100 limiting slenderness values for the strength evaluation of composite CHS beams in bending.