The construction practice of water conveyance tunnels often encounters various complex geotechnical engineering conditions, which bring huge challenges to the design and construction of water conveyance tunnels. Based on the theory of rock elastic–plastic mechanics and finite element analysis technology, this article carried out investigations of engineering geological features, geological formations and hydrological conditions establishes a calculation model for the 3# water conveyance tunnel of the Fenhe River Diversion Project, and analyzes the variation law of surrounding rock stress and displacement during TBM excavation of the tunnel. The results indicate that the dominant direction of the rock mass principal stress measured by the hydraulic fracturing method is NE84°, and the maximum horizontal principal stress, minimum horizontal principal stress, and vertical stress decrease sequentially, analyzing the characteristics of shield TBM construction technology, it is applied to the construction of water transfer tunnels. The numerical simulation of TBM construction using FLAC3D software shows that as the excavation surface advances, the subsidence value of the tunnel roof first slowly increases, then rapidly increases, and then tends to stabilize. The horizontal displacement of the surrounding rock is increasing. The maximum principal stress of the surrounding rock gradually increases. The final surrounding rock stress is 35 MPa. The TBM shield machine with mud water balance driven by indirectly controlled frequency conversion motor is selected for TBM construction of the tunnel. The study offers statistical information to support tunneling technology for water conveyance in the geotechnical engineering practice.