Oil shale industry in Estonia is looking at other mining technologies as alternative to strip mining and room and pillar mining methods. One such alternative to the room and pillar method is the punch-longwall mining method. Enefit Kaevandused AS, one of the major oil shale companies in Estonia, plans to employ this technology in exploiting some of its resources in the near future. This thesis examines the different stability problems related to the planned punch-longwall mining project in Narva oil shale mine. Determining optimal chain pillar dimensions and stability of the punch-longwall highwall slope are the main objectives of this project. Rock mechanical analyses have been done and recommendations are made based on the rock mechanical aspect of the mining process. Taavi Lõhmuste is responsible for the chain pillar stability analysis and Ott Oisalu for the punch-longwall highwall slope stability analysis. It is essential to understand the geology of a certain area in order to make accurate stability assessments. Because of the previously stated requirements, the geology of Estonian oil shale deposit is examined in the first part of the thesis in order to determine the geological and rock mechanical conditions to set the foundation for further analyses. In conclusion, for the part of the highwall slope, a properly designed barrier pillar plays a key role in the stability of the slope. After reviewing and analyzing the results of both highwall slope numerical models, it can be stated that the minimum length for the barrier pillar that still will yield in stable highwall slope is 65 meters. For the part of the chain pillars, in conclusion, it can be determined that optimal chain pillar dimensions that should be suitable, from the stability standpoint, are 6x6 meters for 3-entry system and 7x7 meters for 2-entry system (length x width).