The characteristics of structural plane have an important influence on the stress and deformation of deep buried tunnels. With the diversion tunnel of a hydropower station as our research target, by using the numerical method, a study has thus been carried out on the stability of deep buried tunnels with different dip angles of the structural plane and different distances from the structural plane to the tunnels. The results show that the horizontal displacement on the left side and the protrusion on the bottom of the tunnel are significantly smaller than the settlement on the top and horizontal displacement on the right side of the tunnel. The dip angle of the structural plane has a great influence on the displacement of the key parts of the tunnel, while the distance from the structural plane to the tunnel only has a certain effect on the maximum displacement of the top and the right side of the tunnel. With the distance between the structure plane and the tunnel being less than 3 m, the plastic zone expands along the direction of the structure plane. With the distance being more than 6 m, the area and shape of the plastic zone tends to be stable, and the maximum plastic strain decreases to a lower level and remains stable.