Maintaining and strengthening existing structures is a very important issue in terms of extending the service lifespan of structures. Reinforced concrete (RC) beams with dapped ends are frequently found in bridge girders and precast concrete constructions. The reduction in depth near the supports of RC beams tends to produce a stress concentration and hence requires special analysis and detailing of the reinforcement, especially in the case of torsional stresses. This paper introduces an experimental investigation for the torsional behaviour of recessed RC beams. Along with a control specimen, three beams strengthened using different techniques (the application of fibre-reinforced polymer (FRP) sheets, FRP laminates and external prestressed steel) were constructed and tested under torsion. The results of the research showed that the external prestressing technique produced a higher ductility than the other techniques. On the other hand, the use of external prestressing and carbon fibre-reinforced polymer (CFRP) wrapping to strengthen RC dapped beams subjected to torsional moment increased cracking and failure loads compared with the use of externally bonded CFRP laminate. A three-dimensional truss model is presented to calculate the forces in the stirrups and the ultimate loads for the external prestressing technique. The model shows good agreement with the experimental results.