Optical fiber sensors are newly established gas pipeline leakage monitoring technologies with advantages, including high detection sensitivity to weak leaks and suitability for harsh environments. This work presents a systematic numerical study on the multi-physics propagation and coupling process of the leakage-included stress wave to the fiber under test (FUT) through the soil layer. The results indicate that the transmitted pressure amplitude (hence the axial stress acted on FUT) and the frequency response of the transient strain signal strongly depends on the types of soil. Furthermore, it is found that soil with a higher viscous resistance is more favorable to the propagation of spherical stress waves, allowing FUT to be installed at a longer distance from the pipeline, given the sensor detection limit. By setting the detection limit of the distributed acoustic sensor to 1 nε, the feasible range between FUT and the pipeline for clay, loamy soil and silty sand is numerically determined. The gas-leakage-included temperature variation by the Joule-Thomson effect is also analyzed. Results provide a quantitative criterion on the installation condition of distributed fiber sensors buried in soil for the great-demanding gas pipeline leakage monitoring applications.