Sand production is a worldwide phenomenon that impacts the service life of oil and gas wells, being present in intervals of poorly or unconsolidated rocks. When sand production occurs, some elements are included with the completion structures, intending to stop the produced solids from entering the well. One of them is gravel packing, which consists of a mechanical filter composed of a steel screen and a granular packing. Predicting the behavior and properties of this package is a challenge. Thus, this paper proposes an anisotropic constitutive model to describe the mechanical behavior of a granular package used in an open-hole gravel pack completion. The mechanical properties of the model are calibrated with the literature results of a polyaxial test on a synthetic sandstone cube. In the test, sample loading is divided into two steps. The first one is under confining stress up to a specific limit, and the second increases stress only in the vertical direction. The numerical model adopts a nonlinear elastic behavior in the gravel packing to simulate the effect of the compaction and the increase of particle contacts. Since the stress in the second phase is vertical, causing the arrangement of grains to be greater in one direction than in the other, the gravel packing is considered anisotropic. The study compares the induced displacements in each loading step with excellent agreement between the numerical and available experimental data. Finally, the proposed approach is an attractive alternative to predict the mechanical behavior of gravel packing with good accuracy.