Rock masses with remarked rock structure are likely to be highly anisotropic; thus, the relative orientation of the tunnel with respect to the rock structure will affect the tunnel behavior. Displacements measured at the walls of tunnels in highly anisotropic rock masses often reveal an asymmetric deformation pattern around the tunnel perimeter, which is often interpreted as the result of rock heterogeneity or changing geology. However, numerical and analytical investigation of tunnels in anisotropic rock masses show that the tunnel axis misalignment with the principal directions of stress and material anisotropy induce anti-symmetric axial displacements (i.e., axial distortion of the tunnel cross section) far behind the tunnel face. Near the face, the axial distortion is partially constrained, causing asymmetric radial displacements. In this study, tunnels excavated with and against dip of the major rock mass discontinuity are explored using 3D FEM modeling. A detailed analysis on the mechanisms associated with the direction of excavation is provided. It is shown that the asymmetric displacements near the face may strongly affect the displacements measured at the tunnel walls, which may explain the asymmetric displacements commonly observed on tunnels in anisotropic rock.