This work presents a finite element approach to the three-dimensional static and dynamic response calculations of slender structures totally or partially immersed in a moving fluid. The technique is based on the separation of rigid body motions from the element total displacements resulting in those that effectively cause strain, and which are assumed infinitesimal, under conditions of finite rotations. The position of the structure is defined by a set of co-rotational axes and the evaluation of the finite rotations of this system is detailed. The study considers the non-linearities due to change in geometry, coupling between the axial and bending stiffness mechanisms and the velocity-squared drag loading. For the spatial discretization of the equilibrium equations, the small strain hypothesis is employed. The use of the co-rotational coordinate system makes possible to consider a two node element based on the Euler-Bernoulli beam kinematic model, with cubic Hermitian interpolation functions for the nodal displacements obtained at the convective coordinate system of each element. The Newmark step-by-step scheme is applied to directly integrate, in the time domain, the equilibrium equations and the Newton-Raphson iterative algorithm employed t solve the resultinh incremental non-linear set of equations, at each time step. The presented procedure was implemented in a computer program and various example results were satisfactorily tested against the ones obtained from independent programs.