Abstract <p>The advancement of the oil and gas industry represents a significant priority area for the Russian Federation. Seismic exploration is one of the most prevalent techniques employed in the search for oil and gas deposits. The presence of porous and fractured heterogeneity in the geologic structures is directly correlated with the occurrence of these deposits. The presence of fractures in the medium gives rise to anisotropy, which may be defined as the dependence of the speed of wave propagation on their direction. This phenomenon enables the utilization of seismic data for the reconstruction of the structural and geological characteristics of the area under investigation. This article presents a numerical study of anisotropy in wave propagation velocity in a fractured medium. The grid-characteristic method was employed to address this issue. In this study, a grid model of the medium was constructed, as well as a model of the fracture that considers the width of its opening. Numerical experiments were conducted to model the propagation of elastic waves in the medium, and the anisotropy parameter was measured. The obtained results were compared with those of the real experiment and the predictions of theoretical models.</p>