Dynamic motion of two flexible fibers settling in an infinitely long fluid column at moderate Reynolds numbers is numerically simulated in a three-dimensional space by using a lattice-Boltzmann latticespring method. In the simulations, rectangular and cylindrical flexible fibers are used. The fiber rigidity, density, shape, initial distance, and aspect ratio are varied at different levels and their effects on drafting, kissing, and tumbling (DKT) behavior are studied. It is demonstrated that the fiber rigidity has a profound impact on settling velocity, fluid structures, and DKT phenomenon.