A flexible fiber model has been implemented in a general purpose open-source Computational Fluid Dynamics code. The fibers are modeled as chains of cylindrical segments, and all the degrees of freedom necessary to realistically reproduce the dynamics of real fibers, are taken into account. Each segment is tracked individually and their equations of motion account for the hydrodynamic forces and torques from the interaction with the fluid, the elastic bending and twisting torques, and the connectivity forces and moments that ensure the fiber integrity. The segment inertia is taken into account and a one-way coupling with the fluid phase is considered. The model is applied to simulate the rotational motion of an isolated fiber in a low segment Reynolds number shear flow. In the case of a stiff fiber, the computed period of rotation is in good agreement with the one computed using Jeffery’s equation for an equivalent spheroid aspect ratio. A qualitative comparison is made with experimental data for flexible fibers. Further, a generic test case is described and used to validate the energy conservation and the response time of the fiber model concept. These results show that the implemented model can reproduce the known dynamical behavior of rigid and flexible fibers successfully.