To provide sustainable reinforced concrete deep beams, the replacement of steel rebars by FRP rebars with high-chemical resistance is proposed by researchers. However, the effects of the concrete strength, top and web longitudinal reinforcements, and types of FRP flexural rebars on the non-linear performance of concrete deep beams have rarely been evaluated. This study numerically assessed the effects of the top and web longitudinal reinforcements and concrete strength on the non-linear behaviour of GFRP- and CFRP-strengthened concrete deep beams with various shear span-to-overall depth (a/h) ratios. As per the results, the highest tensile stress was obtained for the steel reinforcement, and the tensile stress in the CFRP reinforcement was more than that of the GFRP reinforcement under the failure load. Meanwhile, the results of high- and normal-strength concrete deep beams with the web reinforcement (16.4%) were lower than those without the web reinforcement (22.3%). Therefore, the web reinforcement moderately compensated for the low strength of normal concrete and the absence of the top longitudinal rebar to reinforce concrete deep beams in carrying the ultimate load. Furthermore, the participation of the GFRP reinforcement with the high-strength concrete was more than that with the normal-strength concrete in carrying a higher amount of loading.