The mechanical interactions between fibers in a dense random-fiber network transmit stress, cause fiber curvature, and influence fiber orientation in the processing of many types of composites. A few theories describe the mechanics of fiber networks, but almost no simulation results are available. Here, we report a direct numerical simulation of the mechanical behavior of random-fiber networks. The finite element method is used, and each fiber is represented by a small number of 3D beam elements. The calculations assume a periodic structure to avoid boundary effects, but within the unit cell, the fibers are placed randomly. A special algorithm that uses the random sequential adsorption process creates an initial structure of straight, random, nonintersecting fibers from which a unit cell with periodic boundary conditions is built automatically [A. I. Abd El-Rahman and C. L. Tucker III, "Mechanics of random discontinuous long-fiber thermoplastics. Part I: Generation and characterization of initial geometry," ASME J. Appl. Mech. (2013)]. The simulation uses an explicit time integration of dynamic equations, with a general contact algorithm (ABAQUS/Explicit). A typical run involves 5000 fibers with l/d = 100, compressing the network from an initial volume fraction of 5% to a final volume fraction of 25% using 10(5) time steps. At the final volume fraction, there are 200 000 fiber-fiber contacts. Results from the simulation are in good agreement with van Wyk ["Note on the compressibility of wool," J. Text. Inst. 37, T285-T292 (1946)] theory for compaction pressure at low-to-moderate fiber density. They show fair agreement with Toll ["Packing mechanics of fiber reinforcements," Polym. Eng. Sci. 38(8), 1337-1350 (1998)] theory for the number of fiber-fiber contacts, and they also show good agreement with a simple slender-body model for fiber orientation, at least during the initial uniaxial compression. This simulation provides an interesting tool for understanding the mechanics of random-fiber networks and building models of composite materials processing. (C) 2013 The Society of Rheology.