In-Situ Resource Utilisation and Off-Earth mining require the application of horizontal drilling. The stability of such openings is challenging when excavating in the lunar regolith. Excavations on the Moon will encounter unconventional operational conditions such as different material properties, low gravity, and a moonquake. Micro-tunnelling or drilling to support lunar exploration and development of infrastructure on the Moon requires stability analysis to ensure its desired performance. The discrete element method (DEM) modelling technique has been utilised to investigate the optimum opening sizes on the lunar soil. From the literature, the mechanical properties of the lunar regolith have been reviewed and used for numerical model development. The model has been calibrated by simulating numerical triaxial tests with the Mohr–Coulomb failure criterion. Then, detailed parametric studies have been performed to investigate the influence of confinement, opening dimensions and moonquakes on the stability of openings. The findings have led to the development of a simple stability chart of the relationship between unsupported opening sizes and lunar regolith properties at different depths.