Understanding and interpreting the location, intensity, and aperture of tectonic fractures within deep geological structure are important to hydrocarbon exploration and development. Taken the Paleogene tight sandstones interbedded with mudstone interlayers in Tarim Basin as an example, we explored a novel finite-element-based geomechanical modeling to quantitatively predict fracture development and distribution, and effectively evaluate the vertical penetration of fractures through mudstone layers. This approach is based on the concept that fractures can be inferred from the redistribution of stress and strain with combination of certain failure criterion. We established several sets of sand-shale interbedded geological models and compared simulation results with observed core data. It was found that in tight sandstone reservoirs with few ductile interlayers, the elastic parameter is main factor affecting development of fractures. In contrast, the sand/mud thickness ratio is the most important factor controlling the development of fractures for sandstone interbedded with multiple mudstone layers. Furthermore, the lithology of interface/boundary was shown to strongly control the fracture penetration into mudstone interlayers. When the mudstone interlayer is thin enough, it is easily penetrated by fractures generated in sandstones, and fractures are more likely to develop around lithological interface. Such results were explained by the differences in rock mechanics properties and inconsistent deformation between layers and its derived tensile stress. The modeling results on fracture density and aperture showed good agreement with the core observation and micro imaging interpretation, and the average simulation accuracy of single wells has reached more than 80%.