For many applications in geotechnical engineering, an accurate assessment of soil hydraulic conductivity is important to predict settlements and pore water pressure changes. Laboratory test data can inform the permeability parameters adopted in finite-element analyses; however, the anisotropy and evolution of permeability during deformation cannot be easily measured. In this study, the influence of shearing on permeability and its anisotropy in medium-loose liquefiable sands is investigated. The discrete-element method (DEM) is used to simulate monotonic undrained and drained triaxial tests using spherical particles. Finite-volume (FV) simulations using computational fluid dynamics (CFD), and pore network model (PNM) simulations are undertaken to evaluate permeability in three orthogonal directions at different strain levels. The results indicate that shear deformation induces anisotropy in permeability, in both drained and undrained triaxial conditions, and this anisotropy increases with axial strain. Specifically, the results show an increase in permeability in the direction of the major principal stress, whereas a reduction in permeability is observed in the orthogonal plane. Undrained variations are purely driven by fabric, whereas drained changes are strongly influenced by volumetric strain. In both cases, a consistent distortion in both the pores and the constrictions or throats connecting adjacent pores is observed. The small magnitude of the changes suggests that for many, coupled finite-element analyses accounting for the evolution of permeability anisotropy during shear deformation may not be necessary. However, the combination of high-resolution FV simulations with computationally efficient PNM simulations allow to analyze the driving mechanisms of flow in granular materials and to verify the applicability of PNM in medium-loose assemblies. The assumption of constant volume accurately captures the sudden loss of contacts at the onset of liquefaction, but cannot reproduce the permeability changes observed in centrifuges and field tests. Results indicate that the Kozeny–Carman (KC) framework can be used to describe isotropic and shearing permeability changes, if variations in tortuosity and pore shape factor are accounted.