This paper studies the influence law of existing tunnels on the construction of intersecting new tunnels in a shallow slope burial context through 3D numerical analysis. The emphasis is on exploring the effect of new tunnels constructed in 54 conditions, including three ratios of overburden to tunnel height (C/H), three ratios of slope distance to tunnel span (D/W), two backfilling conditions of the existing tunnel (“hty” and “htn” conditions), and three magnitudes of surface loads (10 kPa, 20 kPa, and 30 kPa), on the deformation of lateral slopes and the overlying road. As the results show, the rigidly separated area between the existing and newly built tunnels in parallel to the excavation direction was precisely the sensitive area affected by the existing tunnel backfilling condition. The road settlement simulations perpendicular to the excavation direction revealed that various C/H and D/W ratio combinations controlled the shape and size differences of the settlement trough curve. This was because the C/H ratio primarily controlled the effective span and height transition of the newly built tunnel, whereas the D/W ratio mainly controlled the intersection position of the tunnels. Next, model A-A (“hty” condition) was identified as the only feasible construction model among all models in accordance with the engineering safety control criteria. Lastly, comparison of monitoring data with simulations found a slight difference in the distribution pattern between the two. Nevertheless, the final maximum settlement fully satisfied the construction control requirements overall. Aside from proving the correctness of simulation results, the present study also sets an excellent referential example for similar projects.