A model for flexible fibers in viscous fluid flow is proposed, and its predictions compared with experiments found in the literature. The incompressible three-dimensional Navier-Stokes equations are employed to describe the fluid motion, while fibers are modeled as chains of fiber segments, interacting with the fluid through viscous and dynamic drag forces. Fiber segments, from the same or from different fibers, interact with each other through normal, frictional, and lubrication forces. Momentum conservation is enforced on the system to capture the two-way coupling between phases. Quantitative predictions could be made, and showed good agreement with experimental data, for the period of Jeffery orbits in shear flow, as well as for the amount of bending of flexible fibers in shear flow. Simulations, using the proposed model, also successfully reproduced the different regimes of motion for threadlike particles, ranging from rigid fiber motion to complicated orbiting behavior, including coiling and self-entanglement.