During the service life of a building structure, the introduction of web openings into existing steel floor beams is often required to allow for new services such as air conditioning, sprinkler systems, telecommunications etc. However, the presence of large openings in the webs can significantly reduce the shear and bending strength capacity of the beams. Traditionally, the welding of additional steel plates around the opening areas is adopted as a means of strengthening and stiffening. This not only presents practical difficulties but can induce residual stresses which weaken fatigue performance of the section. The aim of this study is to explore the applicability of externally bonded carbon fibre reinforced polymer composites (CFRP) as an alternative means of strengthening for web openings in steel flexural elements. A numerical and experimental investigation was employed in the research reported in this thesis to achieve this aim. Using a non-linear finite element approach, the effects of strengthening arrangements and CFRP lengths were investigated with a view to determine the most structurally efficient layout of CFRP strengthening. The experimental tests were conducted later on four specimens, one control specimen (without opening and un-strengthened) and the rest with different web opening positions and CFRP strengthening. In order to further understand the limits of applicability of this approach, further numerical modeling was also performed to assess the proposed strengthening method when applied to full-scale steel beams with web openings at mid-span or in the high shear zone. The series of beams examined comprised the types of spans which are common in commercial frame buildings. The outcomes of this research show that the CFRP strengthening method is capable of recovering and in some cases exceeding the strength of the beam to that before the introduction of web openings. Similarly, the strengthening method increases the stiffness of the altered beam, thus bringing deflections back to a level similar to the beam before introduction of openings. In many of the strengthened cases, a reduction in ductility was observed; this can in part be due to over-specification of strengthening thickness and thus demonstrates the importance of choosing the optimum strengthening arrangement. In parallel with the reduction in ductility, it was observed that changes in failure mode and position can occur with certain strengthening arrangements in comparison to the unaltered beam. In the application of the method to full scale beams, the results of the simulations suggest that the technique of CFRP strengthening can be used effectively as a realistic and practical alternative solution to retrofitting of existing steelwork. When the CFRP strengthened beams were compared to those with traditional welded steel plate strengthening designed according to SCI P355 (2011), the results were found to be similar in terms of load capacity and overall failure mode.