Roof falls and accumulation of dangerous gasses are the most common hazards in any underground coal mine. Different mechanisms can jeopardize the stability of the roof in underground excavations and successful roof control can only be obtained if the failure mechanism is identified and understood properly. The presence of discontinuities, the inherent variability of the rock mass and discontinuity properties, and the uncertainties associated with directions and magnitudes of the in-situ stress makes the rock engineering problems challenging. The numerical modeling can assist the ground control engineers in designing and evaluating the stability of the underground excavations. If extensive geological and geotechnical data are available, then detailed predictions of deformation, stress and stability can be accomplished by performing numerical modeling. If not, still the numerical modeling can be used to perform parametric studies to gain insight into the possible ranges of responses of a system due to likely ranges of various parameters. The parametric studies can help to identify the key parameters and their impact on stability of underground excavations. The priorities of the material testing and site investigation can be set based on the selected key parameters from parametric studies. An underground coal mine in western Pennsylvania is selected as a case study mine to investigate the underlying causes of roof falls at this mine. The immediate roof at the case study mine consists of laminated silty shale, shale, or sandstone that changes from area to area, and the floor is shale or soft fireclay. This study was mainly focused in the stability analysis of the roofs with the laminated silty shale rock type, where the majority of roof falls had taken place in the roof with this type of roof material. Extensive laboratory tests were performed on the core samples obtained from the case study mine to estimate the intact rock and discontinuity properties of the materials that occur in large extent at the selected interest area of the case study mine. In this research, the three-dimensional distinct element method was used to investigate the stability of the roof in an underground room-and-pillar coal mine. The implemented technique was able to accurately capture the failure of the major discontinuities and rock masses which consist of intact rock and minor discontinuities. In order to accurately replicate the post failure behavior of the rock layers in the immediate roof area, the strain-softening material constitutive law was applied to this region. Extensive numerical parametric studies were conducted to investigate the effect of different parameters such as the variation of immediate roof rock mass strength properties, variation of discontinuity mechanical properties, orientations and magnitudes of the horizontal in-situ stresses, and the size of pillars and excavations on stability of the excavations. The distribution of post failure cohesion along with other measures such as accumulated plastic shear strain, distribution of Z-displacements at the roofline, failure state (joint slip and tensile failure) and displacement (normal and shear displacements) of discontinuities were used to accurately assess the roof stability in this case study. The research conducted in this dissertation showed that the bedding planes play an important role on the behavior of roof in underground excavations. Therefore, an appropriate numerical modeling technique which incorporates the effect of discontinuities should be employed to simulate the realistic behavior of the discontinuous rock masses such as the layered materials in roof strata of the underground coal mines. The three-dimensional distinct element method used in this research showed the clear superiority of this technique over the continuum based methods.