Strengthening reinforced concrete (RC) beams using externally bonded steel plates or fibre reinforced polymer (FRP) composites to enhance their structural performance has been paid great attention in recent years. RC beams strengthened in such way (plated RC beams) have many failure modes different from those of conventional concrete beams. A better understanding on the behaviour of the strengthened beams is essential for safe and economical design of strengthening schemes. This thesis presents research into discrete crack modelling of plated RC beams using a specialised computer program developed in this research. A key factor affecting the behaviour and reliability of strengthened concrete structures is the bond strength between the steel or FRP plate and the concrete substrate. A literature review has shown that many different methods have been used to test this bond strength. An extensive analysis on the stress distribution in various test set-ups was conducted using the finite element analysis (FEA). Results show that stress distribution can be significantly different among different set-ups, for similar materials and geometry. The bond strength and failure modes can be significantly dependent on the adopted test method. These suggest that it is important to develop a standard test method so that test results from different sources are comparable. The research studied a number of issues in using a discrete crack model based FEA method to model the behaviour of plated RC beams: Firstly, extensive FEA carried out in this research shows that the accuracy of predicted stress intensity factors may be significantly improved by adding a rosette around the crack tip in linear elastic fracture mechanics (LEFM) problems, but the optimum rosette size is problem dependent. In order to avoid this uncertainty, a new procedure was devised which resulted in good predictions even for very coarse meshes. Secondly, a mixed-mode discrete crack LEFM based FEA model was developed to model the behaviour of plated RC beams. Automatic multiple crack propagation during the whole loading process until the failure of the structure was modelled. Simulation of the concrete cover separation failure mode has been particularly success. Numerical results confirmed that the bonding of a plate leads to smaller and more closely spaced cracks than the un-strengthened beam. For plated beams, the cracking can have significant effect on the stress distribution in the FRP plates. The length of the plate has a significant effect on the failure mode. Finally, 16 numerical strategies were compared for solving problems associated with sharp snap-back behaviour encountered in modelling discrete crack propagation in concrete beams using non-linear fracture mechanics. A four-point single notched shear beam with nonlinear interface elements representing the discrete cracks was used for this purpose. The results show that the effectiveness and efficiency may vary considerably from one to another, with the local arc-length based procedures in conjunction with tangential stiffness strategy and reversible unloading model being the most robust.