Low-density granular soil in partially saturated conditions can experience static liquefaction due to its contractive tendency when subjected to undrained shearing. This process can lead to saturation of the partially filled voids and the subsequent compressive volumetric strains may induce an increase of pore water pressure with a reduction of effective stress and strength. In this study, an advanced constitutive model (Tasiopoulou & Gerolymos, 2016) able to simulate the liquefaction phenomenon is exploited and extended to be applied to both saturated and unsaturated states of soil. To do that, the model has been formulated in terms of Bishop’s stress (Bishop, 1959), allowing to consider the increments of the elastic stiffness and strength induced by suction. The model is incorporated into the open-source code Anura3D (www.anura3d.com), based on the material point method (MPM) (Sulsky et al., 1994) and developed to deal with large deformations and soil–water-structure-interaction problems. The soil is modelled with the MPM “2 phase–1 point” formulation with suction effect (Ceccato et al. 2021). In this simplified approach the gas pressure is assumed constant and the degree of saturation, depending on suction through water retention curve, is taken into account in the liquid phase mass balance equation. Experimental undrained triaxial stress paths are simulated to assess the capabilities of the implemented constitutive model to simulate the liquefaction potential of partially saturated soils focusing on the effect of the degree of saturation. Affected by the air partially filling the voids, the stress paths initially approach the drained response and, as the degree of saturation increases, they finally tend to the saturated undrained response. Finally, the numerical tool proposed is applied to simulate the construction process by layering of an embankment inspired by the tailing deposition process and its failure due to static liquefaction.