Fracture networks improve wells’ deliverability of fluids from underground reservoirs. However, conductive fractures may lose efficiency because of fracture closure or formation damage that needs to be monitored and detected for proper reservoir management and intervention. Fracture hydraulic conductivity is a function of fracture geometry and its hydraulic aperture, which tends to degrade during operations because of fracture compaction and closure. Furthermore, pore-clogging of fracture walls (faces) results in a damaging skin zone that may reduce fracture-matrix transmissibility. Current Pressure Transient Analysis (PTA) models in the literature do not consider the interconnected combined effect of stress-dependent conductivity of fractures and fracture face skin. Modeling fracture closure without accounting for the skin effect may mislead the PTA interpretations of well performance. This work proposes a rigorous PTA model to account for fracture closure combined with fracture face skin for single and multistage hydraulic fractures with uniform and complex geometries. The solution approach is based on subdividing the domain into three flow regions, matrix, damage zone, and hydraulic fracture (HF). The proposed model is verified extensively using a commercial simulator and other less comprehensive models from the literature. The pressure response in fractured wells with stress-sensitive fractures is analyzed at early, middle, and late times. In each flow regime, we identify pressure signals to detect fracture closure by incorporating fracture closure and skin effects. Results show that the fracture face skin has a significant effect on fracture performance as it introduces an additional pressure drop that triggers an earlier and more pronounced occurrence of fracture closure. We proposed a semi-log approach to identify fracture closure for low compressible fractures and a pseudo-radial simplification to generate late-time response curves. The proposed method serves as a PTA diagnostic tool to detect fracture conductivity degradation due to fracture closure and formation damage.