Fiber forms the basis for different bio-materials, and studying the motion of fibers suspended in a flow is essential in many industrial applications. For example, in the paper-making industries, the forming process starts from a dilute fiber suspension and ends with a dry sheet. In this process, controlling the orientation distribution and density fluctuation of the fibers in the flow is vital to achieve the target properties of the formed sheet structure. Moreover, the link between the different process parameters, such as flow rate and dewatering conditions of the paper making process, is yet to be established w.r.t. the material properties of the final product. Thus, we aim to have a virtual paper machine and plan to do it thorough the numerical simulations. This work presents a robust computational framework to accurately describe the elastic response of slender flexible structures undergoing finite displacements generated by fluid forces. Within this, we use a general formulation, a geometrically exact beam model, also referred to as the Simo–Reissner beam model, to describe the mechanical behavior of the slender flexible structure [1]. It allows finite strains and makes no assumption on the amount of rotations. The Navier-Stokes equations are used to model unsteady incompressible viscous flow. To realize the coupling between the fluid and the filament, the immersed boundary method is utilized [2]. For the accurate and efficient simulation of the filaments, we resort to the NURBS-based isogeometric analysis technique [3]. The fluid motion is resolved with a pressure projection method on a Cartesian structured grid. The performance and versatility of the developed framework are shown using a few validation cases.