The paper describes the design and construction of a new type of torsional fatigue testing machine of the resonance type capable of generating a reversed harmonic torque of up to ±3 × 106 lb.-in. in a stationary test shaft, at a frequency of approximately 2,500 vibrations per minute. Reference is made to a specially developed electronic method of speed control capable of regulating the nominal stress in the specimen to within one per cent. The paper includes the results of a number of fatigue tests carried out on 9 3/4-inch diameter mild steel shafts, and also on “Meehanite” cast-iron specimens of 6 inches diameter, and concludes with some remarks on scale effect, based on results from 1/2-inch diameter specimens subjected to reversed torsional fatigue tests carried out on a combined-stress fatigue testing machine at the National Physical Laboratory.