This paper develops a novel solution scheme for the analysis of the transfer of an axially symmetric torque from a nonuniform elastic bar into a layered elastic halfspace. The torsional deformation of the bar is specified by a set of kinematically admissible functions that are indeterminate to within a set of arbitrary constants. The embedded bar-elastic halfspace system is represented by extended halfspace and a fictitious bar. The fictitious traction distribution on the extended half-space due to a specified displacement field is determined by a discretization procedure. The results of the analysis is used to develop the total potential energy functional for the bar-elastic halfspace loading system.