In this work, major testing methods for characterizing the pure mode III delamination behaviors of composites are discussed and two Edge-Crack-torsion tests have been realized. Moreover, a new fracture toughness test, the Edge-Ring-Crack-Torsion method (ERCT), has been developed. This is a torsion test on a composite plate containing an edge ring crack between two layers. The loading mode obtained is pure mode III, and the distribution of GIII across the crack tip depends on the lay-up of the laminates used. A comparison of the two former testing methods and ERCT in terms of both experiment and modeling is presented. The importance of tests of mode III delamination is demonstrated by a comparison of the pure mode I, II and III delamination toughness.