Rock bolts have been extensively used as a support element in coal mines in the US for about 40 years. Longwall development and partial extraction room-and-pillar mining systems now rely heavily on fully-grouted roof bolts as the primary support with as needed inclined bolts, trusses, and cable bolts as secondary support. These two coal mining systems develop 3- and 4-way intersections during extraction processes. A study of Illinois (2004--2008) and US coal mines found that over 70% of roof falls occurred at intersections. It is therefore necessary to perform additional research in stress and displacement distributions around intersections and then design support systems to improve stability of intersections. This thesis research, in cooperation with a bolt supplier and NIOSH, analyses the stress and strain redistribution in and around intersections in typical lithologies in the Illinois Basin coal mines with the goal to develop a better understanding of failure initiation and propagation mechanisms with and without roof supports. Analyses were corroborated with field observations wherever possible. Non-linear continuum analyses using the Generalized Hoek-Brown failure criterion with rock mass properties is the foundation for these analyses. The first task (Task 1) toward these goals was to develop rock mass properties from available laboratory data using estimates of Geological Strength Index (GSI) for different lithologies. An important subtask was to perform an error analysis in estimates of rock mass properties assuming an amount of error in GSI estimates. Analyses and field observations were done for typical 4-way intersections at two mines in southern Illinois operating at depths of 150 m and 80 m, respectively in the No. 6 coal seam, which averages 1.8 m in thickness. Pre-mining horizontal stresses of 7.58 MPa and 4.13 MPa were applied in the E-W and N-S directions. These coal companies provided geologic logs and rock mechanics data for roof and floor strata. Rock mass engineering properties for different roof and floor lithologies were developed using estimated values of Geological Strength Index (GSI), and Hoek-Brown (H-B) rock mass failure parameters. A recent laboratory study provided normal and shear stiffness properties of the immediate roof interfaces within the bolting range of 1.8 m. MSHA-approved roof support plans were used for initial modeling. Short Encapsulation Pull Test (SEPT) data provided by bolt suppliers in the region were used to assign bolting system stiffness and strength parameters. Task 2 analyzed normal and shearing stresses and strains in and around mine intersections for typical pre-mining stress fields and then identified critical areas of failure initiation and progressive failure propagation. Failure initiation was hypothesized to occur for critical values of compressive (1 mm/m), tensile (0.5 mm/m), and shearing (0.5 mm/m) strains based on a review of laboratory stress-strain properties. This approach allows quantifying areas in and around an intersection where failures are likely to initiate with and without artificial supports. It computes three reinforcement factors with and without supports: reinforcement against tensile (RFT), compressive (RFC) and shearing (RFSS) strains. Task 3 assessed the performance of currently practiced roof support plans and identified where inadequacies exist and how they could be improved through spatial distribution of supports and their characteristics. Analyses were completed for two mines with one orientation of pre-mining horizontal stress field. The next logical step (Task 4) was to extend analyses in Task 3 to assess the effect of maximum compressive stress orientation in relation to entry direction (0° 30°, 60° & 90°) and different cut sequences and their effect on changes in failure initiation and failure propagation mechanisms. Numerical analyses have shown that stress and strain distributions are significantly different when the cut sequence is included in models. For a horizontal stress ratio of two (2), the 60° orientation provided maximum stability. Separate models with all cuts excavated simultaneously corresponded well with the well-established NIOSH software AHSM and previous research. The effect of cut sequence combined with the directional effect of pre-mining stresses becomes evident from the dissimilar results. A separate statistical study was conducted on 211 SEPT test data provided by a roof support manufacturer and marketing company in the region. Goals were to analyze the database for grip factor (GF) and anchorage stiffness (AS) characteristics using histograms and frequency distributions and, perform regression analyses to relate GF and AS values on the basis of height above coal seam and bolt diameter. Results were used for one stochastic run with variable GF and AS values assigned to different bolts in a roof control plan. Results indicated Gamma distribution best fitted AS and GF data. It was thought that the reinforcement factor for such a bolting layout would be more realistic than assigning a single value of GF and AS to bolts in the model.