A synthesis of well logs was carried out and drilling mud weight data were analyzed to figure out anomalous high fluid pressure within the Triassic evaporitic cap rock (the Dashtak formation) and study its impact on the geometry of anticlinal traps in the gas rich Gavbandi province located in the southeast part of the Zagros Mountains. The results indicated that the location of anticlinal traps at the depth in which the Permian Dehram Group reservoir unit exists is horizontally displaced with respect to surficial crest of many anticlines within the Gavbandi area. This crestal shift may be induced by abnormally high fluid pressure in the “A evaporate” member of the Dashtak formation, detected in many exploration wells across the area. When fluid pressure increases due to compaction during shortening, the higher shaliness could probably cap more fluids and consequently increase the fluid pressure within the Dashtak formation. Anomalous high fluid pressure decreases internal friction and shear strength of rock units and facilitates fracturing and faulting within the Dashtak formation, which consequently causes crestal shift of anticlinal traps. This should be taken into account when planning a new exploration well in Gavbandi area in order to prevent trap drilling.