This paper investigates the possibility of strengthening Reinforced Concrete (RC) beams under pure torsion loadings. The torsional behaviour of strengthened RC beams with near-surface mounted steel and CFRP bars was investigated. The verification with the experimental work was performed to ensure the validity and accuracy which revealed a good agreement through the torque-rotation relationship, ultimate torque, and rotation, and crack pattern. This numerical study included testing of thirteen specimens (one of them was control beams while the remaining 12 were strengthened beams) with several parameters such as mounting spacing and configuration. The analytical results revealed that the addition of NSM rebar redistributed the internal stresses and enhanced the ultimate torsional strength, torque-rotation capacity, ductility, and energy absorption of the concrete beams. Most of the strengthened beams revealed the appearance of the cracks at a phase less than the reference beam by an average of (9%). Concerning the NSM strengthening, the CFRP bars provided a higher enhancement ratio when compared with the beams that strengthened with NSM steel rebar especially for the strengthening space equal to 130 mm and more. The ultimate torsional strength increased by (3.5%) and rotation decreased by (4%) approximately when the steel rebar was replaced by the carbon bar. The ductility and energy absorption of the analysed beams showed that the strengthening enhanced the ductility of the twisted beams. The ductility values varied according to the method of strengthening used, as it showed the highest values of the beam that was strengthened small spacing.