In this study, we purposed to investigate the edge of geostructures and position of existing faults of the Shamakhy-Gobustan and Absheron hydrocarbon containing regions in Azerbaijan. For this purpose, the horizontal gradient, analytic signal, tilt angle, and hyperbolic of tilt angle methods were applied to the first vertical derivative of gravity data instead of Bouguer gravity data. We obtained the maps that show the previous lineaments which were designated by considering the maximum contours of horizontal gradient, analytic signal maps, and zero values of tilt angle, hyperbolic of tilt angle maps. The geometry of basement interface was also modeled utilizing the Parker-Oldenburg algorithm to understand the sediment thickness and coherency or incoherency between the gravity values and basement topography. The lineaments were held a candle to most current tectonic structure map of the study area. It was seen that the techniques used in this study are very effective to determine the old and new lineaments in the Shamakhy-Gobustan and Absheron regions. The epicenter distribution of earthquakes within the study area supports the new lineaments which are extracted by our interpretation. We concluded that better comprehension of Azerbaijan geostructures and its effect on the large scale works will be provided by means of this study.