A particle-level simulation method is employed to study the dynamics of flowing suspensions of rigid and flexible fibers. Fibers are modeled as chains of prolate spheroids connected through ball and socket joints. By varying the resistance in the joints, both flexible and rigid fibers can be modeled. Repulsive interactions between fibers are included, but hydrodynamic interactions and particle inertia are neglected in this implementation. The motion of a fiber is determined by solving the translational and rotational equations of motion for each spheroid. Simulations of isolated fibers in shear flow demonstrate that the method can reproduce known dynamical behavior of both rigid and flexible fibers. The transient behavior in the suspension relative viscosity under simple shear flow was also investigated. An oscillatory response similar to the experimental observations of Ivanov et al. was obtained for rigid fibers. Fiber flexibility reduced the period of oscillation, but had little effect on steady-state viscosities. These results verify that rigid and flexible fibers can be modeled with linked rigid prolate spheroids. Modeling fibers with fewer elongated bodies, as opposed to many spheres, significantly reduces computation time and facilitates the study of suspensions of many interacting, long fibers.