Existing reinforced concrete elements may need strengthening due to increased applied loads or due to deterioration of the reinforcement bars caused by rust, reducing the cross-sectional area. This study focuses on strengthening reinforced concrete beams by adhesively bonding steel plates to different positions of the tension zone, creating composite beams. Plates were bonded horizontally to the soffit; these are referred to as externally bonded (EB) composite beams. Plates can also be placed into a vertical slot cut into the soffit; these are referred to as near-surface mounted (NSM) composite beams. A comparison was drawn in this research study between the flexural resistance predicted by the mathematical model and the experimentally measured results. The predictions of the mathematical model compared very well to the experimentally measured specimens. The EB composite beams yield mathematical results 0.41% higher than the experimental results and the NSM beams 3.69% higher than the experimental results. The experimentally tested flexural resistance of the EB beams is 11.1% higher than that of the NSM composite beams, which is expected due to the larger lever arm of the internal couple to the bonded plate. An increase of 63% in the flexural capacity of the non-plated reinforced concrete beam over that of the EB composite beams was achieved.