The prevailing approach for hydraulic-fracture modeling relies on linear-elastic fracture mechanics (LEFM). Generally, LEFM that uses stress-intensity factor at the fracture tip gives reasonable predictions for hard-rock hydraulic-fracturing processes, but often fails to give accurate predictions of fracture geometry and propagation pressure in formations that can undergo plastic failures, such as poorly consolidated/unconsolidated sands and ductile shales. This is because the fracture-process zone ahead of the crack tip, elasto-plastic material behavior, and strong coupling between flow and stress cannot be neglected in these formations. Recent laboratory testing has revealed that in many cases, fracture-propagation conditions cannot be described by traditional LEFM models. Rather, fractures develop in cohesive zones. In this study, we developed a fully coupled poro-elasto-plastic hydraulic-fracturing model by combining the cohesive-zone method with the Mohr-Coulomb theory of plasticity, which not only can model fracture initiation and growth while considering process-zone effects, but also can capture the effects of plastic deformation in the bulk formation. The impact of the formation plastic properties on the fracture process is investigated, and the results are compared with existing models. In addition, the effects of different parameters on fracture propagation in ductile formations are also investigated through parametric study. The results indicate that plastic and highly deforming formations exhibit greater breakdown and propagation pressure. The more plastic the formation (lower cohesion strength), the higher the net pressure required to propagate the fracture. Also, lower cohesion strength leads to shorter and wider fracture geometry. The effect of formation plasticity on a hydraulic fracture is mostly controlled by initial stress contrast, cohesion strength of formation rock, and pore pressure. We also found that altering the effective fracture toughness can only partially mimic the consequences of increased toughness ahead of the fracture tip in ductile formations, but it fails to capture the effect of shear failure within the entire affected area, which can lead to underestimating the fracture width and overestimating the fracture length. For a more-accurate modeling of fracturing in ductile formations, the entire plastic-deformation region induced by the propagating fracture should be considered, especially when shear-failure areas are large.