This work presents Tower Flex, a structural dynamics model for a coupled analysis of offshore floating wind turbines consisting of a tower, a floating platform and a mooring system. In this multi-body, linear frequency-domain model, the tower is represented as a series of uniform Timoshenko beams connected to each other. The deflections of the tower are solved analytically in each beam while the mass, damping and stiffness coming from the rotor, the floating platform and the mooring lines are taken into account via generalized boundary conditions. Tower Flex is used for the evaluation of a 3MW offshore floating wind turbine mounted on a Tension Leg Platform (TLP). Natural frequencies, motion responses and fatigue damage are analyzed to illustrate the features of Tower Flex and assess the performance of the proposed design.