This paper discusses a method, based on Nadai’s solution, which can be used to determine the true (Cauchy) shear stress-strain curve of a material by means of torsion test of a solid shaft. The method is shown to be applicable to loading, unloading and cyclic loading. It is also applicable to fixed-end torsion of a solid shaft in the large shear strain range. A modified method has also been derived for the case of free-end torsion of a tubular specimen in the large strain range.