Ground control and stability assessment of underground excavations are among the most critical aspects of underground mining operations. Instability of underground openings not only compromises safety due to potential rock failure and collapse, but also leads to increased operational costs caused by dilution, production delays, equipment damage, and additional waste handling. This issue becomes particularly significant in unsupported (self-supporting) mining methods such as sublevel stoping, where the stability of excavations relies solely on the inherent strength of the surrounding rock mass. In this study, the stability of underground openings in the Tajkuh lead–zinc mine was investigated using numerical modeling. The mine is currently operated at multiple levels with unsupported stopes. Initially, intact cylindrical core specimens were collected from exploratory drilling and subjected to uniaxial and triaxial compressive tests to determine key geomechanical properties, including cohesion, internal friction angle, density, and elastic parameters. Subsequently, numerical simulations were carried out using FLAC2D finite difference software to evaluate the stability of tunnels with different cross-sectional dimensions (2.5×2.5, 3.5×3.5, and 4.5×4.5 m²) at varying depths (30, 55, and 80 m). The results indicate that maximum displacement occurs in tunnels with a cross-section of 4.5×4.5 m² at a depth of 80 m, whereas minimum displacement is observed for tunnels with dimensions of 2.5×2.5 m² at a depth of 30 m. Comparison of the maximum roof displacement with the allowable limits based on the Sakurai criterion demonstrates that all investigated openings remain stable without requiring support systems. Sensitivity analysis further reveals that tunnel stability is more significantly affected by reductions in cohesion and internal friction angle, while increases in these parameters and overburden depth have a less pronounced effect on displacement. These findings provide practical insights into the design and safe operation of unsupported sublevel stopes in carbonate-hosted lead–zinc deposits.