Paperboard is a strongly orthotropic material: Machine Direction (MD) and Cross-machine Direction (CD) are the in-plane directions, with mechanical properties that are in general up to two orders of magnitude higher than in the thickness direction ZD. In-plane deformations and fractures are usually associated to small strains, while large strains and damages are expected in the out-of-plane direction. The in-plane and out-of-plane elastoplastic behavior of paperboard have been considered in several papers, see e.g. Xia et al. (2002), Borgqvist et al. (2015). The purpose of this contribution is to enrich the elastoplastic small-strains 2D model in Xia et al. (2002) with a phase-field modeling of crack propagation. A variational, finite-step formulation of ductile fracture is presented, based on a classical finite-step variational formulation for elastoplastic solids. In the spirit of the phase-field approach to brittle fracture, the energy functional is enriched with a phase-field damage-like variable and with its gradient. Assuming a plasticity-driven crack growth, the damage activation criterion is modified by the addition of a non-variational term, the so called modulation function, depending on a scalar measure of the accumulated plastic strains. This is chosen to depend in a different way on the plastic strains developed in the different material orthotropy directions, so that the introduction of an additional damage variable or of a structural tensor in the gradient damage term is avoided. The model has been validated against results of experimental tests on paperboard and its possible use for prediction purposes has been assessed.