Abstarct: The strengthening or retrofitting of existing concrete structures to resist higher design loads, correct deterioration-related damage, or increase ductility has traditionally been accomplished using conventional materials and construction techniques. Composite materials made of fibres in a polymeric resin, also known as fibre-reinforced polymers (FRP), have emerged as an alternative to traditional materials and techniques. FRP systems have been shown to increase the shear strength of existing concrete beams and columns by wrapping or partially wrapping the members. The aim of this thesis is to investigate the shear behaviour of reinforced concrete beams retrofitted with FRP systems using a nonlinear finite element method (FEM). To perform this analysis, reinforced concrete beams, with and without FRP systems were modelled in ANSYS and FE results were compared with the experimental results published by other researchers. Promising agreement was found between the load-deflection response of the beams resulted by FE analysis and the test results. In the next stage, a parametric study was performed using the calibrated FE model. In this step, the effect of different parameters such as: the configuration of FRP systems in shear strengthening, the thickness and the orientation of fibres and shear span, on the behaviour of reinforced concrete beams retrofitted with FRP was studied.