An imperative task for successful underground mining is to ensure the stability of underground structures, since it influences the safety, and in turn, the production capacity and economic performance of the mine. This is more so for deep excavations in soft rock which may be under significantly high stresses. In this thesis, stability studies on two tunnels, a horseshoe-shaped and an inverted arch-shaped tunnel, have been presented. The tunnels, running at a depth of 1325 m, are part of the Xiezhuang Coal Mine, in the Xinwen mining area, in China. Using the available information on stratigraphy, geological structures, in-situ stress measurements and geo-mechanical properties of intact rock and discontinuity interfaces, a three-dimensional numerical model has been built using the 3DEC 3-Dimensional Distinct Element Code to simulate the stress conditions around the tunnels. Based on available discontinuity geometry constraints, the rock mass has been modelled as a mixture of a discontinuum medium close to the tunnels and as an equivalent-continuum in the far field. Due to the unavailability of field measurements for rock mass mechanical parameters, the parameters have been estimated by incorporating the available intact rock mechanical properties and field deformation monitoring data into a strength reduction model calibration procedure. This back-analysis (calibration) has been carried out through a pseudo-time dependent support installation routine which incorporates the effect of time through a stress-relaxation mechanism. The results from the back-analysis indicate that the rock mass cohesion, tensile strength, uniaxial compressive strength, and elastic modulus values are about 35-45 % of the corresponding intact rock property values. Additionally, the importance of incorporating stress relaxation before support installation in numerical modeling has been illustrated, for the first time in literature, through the increased support factors of safety and reduced grout failures. The calibrated models have been analyzed for different supported and unsupported cases in an attempt to quantify the effect of supports in stabilizing the tunnels and to estimate the adequacy of the existing supports being used in the mine. A direct outcome is that the findings indicate that longer supports may be better suited for the existing geo-mining conditions around the tunnels since they have fractured zones that are larger than the supports currently in use at the mine. The effects of supports have been demonstrated using changes in deformations and yield zones around the tunnels, and changes in the average factors of safety and grout failures of the supports. The use of longer supports and floor bolting has provided greater stability for the rock masses around the tunnels. A comparison between the closure strains in the two differently shaped tunnels indicates that the inverted arch tunnel may be more efficient in reducing roof sag and floor heave for the existing geo-mining conditions. Additional analyses focusing on parametric sensitivity studies on the rock and joint mechanical properties show that the tunnel stability is highly sensitive to changes in cohesion and internal friction angle of the intact rock, and changes in joint basic friction angle. Tunnel stability is seen to not be very sensitive to changes in intact rock tensile strength and joint shear stiffness for the tunnels being studied. Finally, support optimization studies conducted by studying the effect of changing cable diameters and grout uniaxial compressive strengths on support factors of safety and grout failures show the trade-off that is necessary in selecting cable strength vis-à-vis grout strength. The results indicate that simply increasing either one of cable or grout strength parameters without considering their interactions and compatibilities could be detrimental to the stability of the support system.