In this paper, a new continuum-based formulation to obtain the torsional dynamic response of pile foundations is presented. In the analysis, the pile is embedded in a homogeneous soil deposit that is underlain by a half-space. The soil adjacent to the pile is modeled as a three-dimensional (3-D) continuum while the underlying half-space is described by a spring-dashpot system. The 3-D soil continuum follows the Vlasov-Leont’ev foundation model in which the soil displacement field is described as a product of separable functions, and the spring-dashpot system is described by an expression obtained for a torsionally (dynamic) loaded rigid massless disc of infinitesimal thickness bonded to the surface of a homogeneous half-space. In the analysis, the governing differential equations describing pile and soil motions are obtained by applying the Extended Hamilton’s Principle in conjunction with the calculus of variation, which is solved analytically using appropriate boundary conditions. Pile response-complex dynamic pile-head stiffness and distribution of pile rotation and torque with pile embedment depth are obtained from the present analysis and compared with existing solutions in the literature to verify the accuracy of the formulation.