The forced compression behavior of random 3D and 2D pulp fiber networks is investigated. Existing theories are found to describe well the evolution of packing stress with fiber volume fraction for the pulp networks. It was, moreover, found that the packing behavior of an initially random 3D network of pulp fibers does not go through a transition to a 2D network packing behavior as it is compressed. Rather, the fibers exhibit localized collapse at contact points, a result of the hollow nature of the pulp fibers. The implications of this phenomenon on the overall packing response were further examined by means of compression tests performed on a series of representative tubes of varying wall thickness. This analysis allowed determining the pressure range within which localized fiber buckling takes place.