Delivering efficient and cost-effective drilled and excavated holes require effective prediction of instability along the hole profile. Most drilled and excavated hole stability analyses in the literature are performed for a given zone without considering the influence of depth. This study focused on determining the influence of depth on induced geo-mechanical, chemical, and thermal stresses and strains in drilled or excavated holes. To this end, a new porochemothermoelastic model was developed based on extended poroelastic theory, and the developed model was employed in determining induced strains and stresses for an oil and gas well case study, using data from the literature. The study delineated the different significance levels of geo-thermal-, chemical-, and thermal-induced strains and stresses as depth increased. From the results obtained, it was clear that at shallow depths, chemically induced strains and stress were the most significant formation perturbations responsible for instability of drilled and excavated holes. On the other hand, at deeper depths, geo-mechanical-induced strains and stress were the most predominant. Comparatively, thermally induced strains and stresses were found to be the least significant formation perturbations responsible for instability of drilled and excavated holes. For this case study, the results indicated that chemical strains and stresses were more prominent at depths below 170 m, accounting for more than 50% of the total stresses and strains. At 170 m, both chemical and geo-mechanical stress and strain had equal contributions to the overall stress and strain. However, as depth increased, the percentage contribution of the geo-mechanical component increased and accounted for about 80% of the total strains and stresses at 1000 m, which increased to 98.48% at depths of 6000 m and beyond. The findings of this study will provide guide for future studies on the application of extended poroelasticity theory in solving instability problems of drilled and excavated holes.