The s tudy of the torsional oscillation of an elastic solid is important in several fields like soil mechanics, Reissner and Sagoei [1], and mechanical transmission line theory, Macoy [2]. The oscillation of a half-space, excited by a rigidly attached circular disc, were first considered by Sagoci [3] and an approximate treatment of both the oscillating half-space and stratum was subsequently given by Bycroft [4]. Recently, Collins [5] has formulated exactly both the problem as Fredhelm integral equations of the second kind, utilizing methods developed by him [6] and that the of torsion of elastic half space with penny-shape crack and penny-shape inclusion by Dhawan [7], [8]. On the other hand, the mixed boundary value problem for a flat annular rigid stamp was, at first, treated by Gubenko and Mossakovskii [9]. After that, many papers for triple integral equations have been published with relation to the theory of elasticity, fluid dynamics, magnetics, etc. [10]--[16]. In the present paper, we analyzes the three-par tmixed boundary value problem of a transversely-isotropic half-space under torsion by a flat annular rigid stamp on the basis of three-dimensional theory of elasticity. The tangential stress on the stam p is continuous at all points except the inner and the outer edges of the stamp.