The theory of the ring method for measuring shear moduli of wire specimens is developed. The resonant frequencyfsfor oscillations at right angles to the plane of the loop is related to the shear modulusnand Young's modulusEby the equationB&ngr;(&ngr;+7)=2{(2&pgr;2/3)(&ngr;2+2&ngr;+9)+5&ngr;2+46&ngr;+17},in which &ngr; = 2n/EandB=E(a/r)4/2&pgr;(1−h)mfs2·ais the radius of the wire,ris the radius of the loop,mis the mass per unit length of the specimen, andhis a small gap correction term. Measurements of shear moduli on the same wire samples of Cu and Mo by the torsion pendulum and ring methods check within the experimental errors.