The tight gas reservoir in the fifth member of the Xujiahe formation contains heterogeneous interlayers of sandstone and shale that are low in both porosity and permeability. Elastic characteristics of sandstone and shale are analyzed in this study based on petrophysics tests. The tests indicate that sandstone and mudstone samples have different stress-strain relationships. The rock tends to exhibit elastic-plastic deformation. The compressive strength correlates with confinement pressure and elastic modulus. The results based on thin-bed log interpretation match dynamic Young’s modulus and Poisson’s ratio predicted by theory. The compressive strength is calculated from density, elastic impedance, and clay contents. The tensile strength is calibrated using compressive strength. Shear strength is calculated with an empirical formula. Finally, log interpretation of rock mechanical properties is performed on the fifth member of the Xujiahe formation. Natural fractures in downhole cores and rock microscopic failure in the samples in the cross section demonstrate that tensile fractures were primarily observed in sandstone, and shear fractures can be observed in both mudstone and sandstone. Based on different elasticity and plasticity of different rocks, as well as the characteristics of natural fractures, a fracture propagation model was built.