Abstract <p>The study of fingering during fluid displacement in the pores of a porous medium is crucial, particularly in applications such as enhanced oil recovery, groundwater remediation, and carbon dioxide sequestration. This paper investigates the fingering phenomenon that occurs in a Hele-Shaw cell when air displaces glycerin. The research employs both computer simulations and analytical methods to describe the conditions of viscous fingering phenomena, comparing the results from both approaches. The fluid movement equations in the porous medium are derived from the two-phase Darcy’s law, while the fluid interface is captured using the Volume of Fluid (VOF) method. A comparison is made between the outcomes of numerical simulations and analytical methods based on the Saffman–Taylor instability model. As the pressure difference increased, the numerical simulations reported a wider gap compared to the derived analytical results. This discrepancy was attributed to the effect of viscosity, which was not accounted for in the numerical modeling. The findings indicate that the analytical model demonstrated better accuracy within a pressure difference range of 40 Pa.</p>