The main focus of this study is on application of the enhanced embedded discontinuity approach to the analysis of pre-existing fractures. The J-integral is used to evaluate the energy release rate around the crack tip and its value is compared with both that obtained from Extended FEM simulations as well as from an analytical solution. The approach is also used for modeling of cohesive crack propagation. It is demonstrated that the framework gives results that are very close to those obtained using Extended FEM, while the former requires less computational effort. A comparison with a standard smeared approach is provided in order to highlight the nature of the contribution. The embedded discontinuity framework is also applied to flow problems with pre-existing cracks. A modified form of Fourier law is introduced and later employed for modeling of heat transfer/flow in the domain that contains thermally isolated/impervious cracks.