Masts, antennas and other appendaged towers connected to offshore platforms are subjected to harsh environmental conditions. In this paper, the dynamic response of such a structure is investigated. The mast is assumed to be fixed at bottom to an articulated tower and carrying a concentrated mass at the other end. The mast is modelled as a continuous system (beam-like), subjected to wind forces. The equation of motion formulated in this paper is general enough to represent a partially submerged articulated tower or an appendaged tower. In the derivation of the equation of motion, non-linearities due to large lateral displacements as well as rotation, drag wind and wave forces, which are assumed to be proportional to the square relative velocity between the wind/wave and the mast, are considered. The motion of the articulated tower, to which the mast is connected, is also included in the dynamics as a base excitation. The non-linear partial differential equation of motion is then non-dimensionalized and simplified to show that the rotation (inertia) term is negligible. The equation of motion is numerically solved using finite difference approximations, which are embedded in the commercial code ''ACSL'' (Advanced Continuous Simulation Language). The response of the mast to deterministic and random wind and wave is investigated and some parameter studies are conducted. Bending and shear stresses are calculated for different environmental conditions. The model was also used to verify the rigid body assumption frequently used in analyzing the response of a partially submerged articulated tower.