Hydraulic fracturing is used extensively in oil and gas industry to stimulate wells and enhance production, in mining industry to create caving for ore body extraction and for in-situ stress measurements in geotechnical works. Conventionally the modelling of fracture in intact material is based on linear elastic fracture mechanics concepts. The problems with this approach are- i) this fracture mechanics does not consider the influence of the crack tip fracture process zone (FPZ) ii) under high confining stress sedimentary rocks can behave in more ductile manner, similar to a soil, hence the applicability of linear elastic fracture mechanics is questionable and iii) the application of linear elastic fracture mechanics requires mesh rezoning as the crack propagate, hence not suited for multiple crack initiation and propagation, and consideration of fluid flow through newly formed cracks is cumbersome. So, this research will use 'cohesive crack model' to simulate fracture development in these rocks which can cater for both linear elastic behaviour and material plasticity. We aim to develop cohesive crack properties for economically important sedimentary rocks under both Mode I and Mode II and mixed mode fractures. The cohesive crack models will be developed using finite element/finite difference involving material discontinuities. This research is expected to develop a better fracture modelling approach which can be successfully applied to geothermal energy systems, rock slopes in mining, grouting or liquid or gas pumping operations such as in carbon dioxide sequestration, pressuremeter or packer testing, and hydraulic fracturing in oil or gas production.