This theoretical investigation determines the hydrodynamic field interior and exterior to an oscillating viscous drop for the case in which the hydrodynamic field exists strictly as a result of forcing by a modulated acoustic standing wave field. Perturbation of the governing equations of fluid motion generates a hierarchy of systems of equations. At second order, this system represents the hydrodynamic field which is forced by terms quadratic in acoustic field quantities. Viscous effects are incorporated into the acoustic field. Of particular interest is the nature of the hydrodynamic field in a sublayer region which exists near the drop-host interface. The boundary conditions, which are imposed at the drop-host fluid interface and which include the radial and tangential forcing due to the acoustic radiation pressure vector, complete the problem formulation.