This thesis presents numerical and analytical investigation of the geomechanics underlying longwall mining. It was tried out to study the disturbances induced by longwall mining in nearby rocks and their influence on the stability of the gates, pillars and main tunnels of longwall mines. The thesis consists of two major parts: numerical and analytical investigations. The study site is the Svea Nord coalmine, Svalbard, Norway. A novel algorithm was proposed for numerical simulation of the longwall mining process. In the proposed algorithm progressive cave-in and fracturing of the roof strata, consolidation of the cave-in materials and stress changes are simulated in detail. In order to outline the caved-in roof rocks a criterion based on maximum principal strain (in tension) was used. The critical tensile strain of roof cave-in was determined through back-calculation of the surface subsidence above a longwall panel at the mine. The results of the simulations were then used to analyse stress changes induced by longwall mining and the stability of gates. The simulations revealed that the stability of the gates and the loading to the rock bolts are closely related to the width of the chain pillars. With slender pillars, shear displacements along weak interlayers and bedding planes result in heavy loading to the rock bolts. Therefore, the locations of weakness zones should be taken into account in rock bolt design. The developed algorithm was implemented to study the loading and stability of the barrier pillar of the mine. The barrier pillars protect the main tunnels and border area of the mine from disturbances induced by longwall mining in the panels. The simulations show that the stresses in the barrier pillars fluctuate up and down during mining because of periodic cave-in events behind the longwall face. A failure zone of about 12 m exists in the wall of the barrier pillars. A large portion of the barrier pillar is still intact and is, thus, capable of protecting the border area. The results of the detailed simulations of longwall mining via the developed algorithm were, also, implemented in a large-scale numerical model. The model consists of all of the longwall panels and the border area of the mine. It is intended that the coal in the border area on the other side of the longwall panels will be mined after completion of the longwall mining. There is concern about how the longwall mining affects the stress state in the border area and how stress changes would affect future mining in the border area. A failure zone of about 20 m developed in the wall of the main tunnels on the side of the border area after all the longwall panels were mined out. The stress state in the remaining portion of the border area remains unchanged. Therefore, it will be possible to mine the border area in the future. In order to investigate the roof strata cave-in mechanism in detail a discontinuous numerical simulation of roof cave-in process was conducted by UDEC code. The block size in the roof strata and the mechanical parameters of the discontinuities were obtained through back-calculations. The back-calculations were conducted with a statistical method, Design of Experiment (DOE). Numerical simulations revealed that jointed voussoir beams formed in the roof strata before the first cave-in. Beam bending results in stress fluctuations in the roof strata. The maximum deflection of a roof stratum at the study site before the first cave-in is about 70% of the stratum thickness. The simulations and field measurements show no periodic weighting on the longwall shields in this mine. Numerical sensitivity analyses show, however, that periodic weighting may occur in strong roof strata. Roof strata with a high Young’s modulus and large joint spacing are not suitable for longwall mining. The maximum sustainable deflection of the roof strata before cave-in depends upon the horizontal in-situ stress state. It slightly increases with the in-situ horizontal stress in the stratum beams, but the horizontal stress would increase the possibility of rock-crushing in deflected roof beams. The implemented numerical method would be useful in assessment of the cavability of the roof strata and in selection of longwall shields with adequate load capacity. As shown through discontinuous numerical simulations, the roof strata above the underground opening constructed in the stratified rocks form voussoir beams. The stability of those beams is the major concern in the study of the gate stability and roof cave-in assessment in the longwall panels. Two different analytical methods were developed for cases with and without the in-situ horizontal stress acting along the beams. In the analytical model for the beams without horizontal stress a bilinear shape was assumed for the compression arch generated within the voussoir beams. The stability of the compression arch is governed by the energy method. The model requires an iterative procedure for convergence, and an algorithm was proposed for it. The analytical method was verified with numerical simulations by means of a discrete element code, UDEC. For the beams subjected to in-situ horizontal stress, the classic beam theory was employed to drive the analytical solution for it. The superposition method was used to obtain bending/deflection equations of the beam. The validity of both the assumptions and the developed method were, also, investigated by numerical simulations. The developed analytical method revealed that high Young’s modulus of a beam rock increases the stability of the beams against buckling but it causes higher stress within the compression arch which increases the probability of crushing failures in the beam abutments and midspan. In-situ horizontal stress along beams increases their stability against buckling and abutment sliding failure, but it raises the possibility of crushing failure at the abutments and the midspan.