This paper presents modal dynamics of floating-platformsupported and monopile-supported offshore turbines, which are gaining attention for their ability to capture the immense wind resources available over coastal waters. Minimal dynamic loads and the absence of instability are imperative to the success of these turbines. Modal dynamics determine both loads and instabilities to a large extent, and therefore must always be analyzed. Also, to model the turbine, several aeroelastic computer codes require modes of the major components, e.g., the rotor blades and the rotor-nacelle support structure. To compute such modes, we used a recently developed finiteelement code called BModes. The code provides coupled modes either for the rotating blades or for the support structure. A coupled mode implies presence of coupled flexural, axial, and torsion motions in a natural mode of vibration. In this paper, we use BModes to provide modes only for flexible towers, which carry head mass (rotor-nacelle subassembly modeled as a rigid body) and are mounted atop either a floating platform or a soilsupported monopile. The code accounts for the effects of hydrodynamic inertia, hydrostatic restoring, and mooring lines stiffness on the floating platform. It also accounts for the distributed hydrodynamic mass on the submerged part of the tower and for the elastic foundation surrounding the monopile. Results are obtained for three turbine configurations: land-based turbine, floating-platform-supported turbine, and monopilesupported turbine. Three foundation models are used for the monopile configuration. Results show that the hydrodynamic and elastic-foundation effects strongly influence the turbine modal dynamics.