Based on the Maxwell visco-elastic constitutive model and the solution of the anisotropic displacement for surrounding rock,the time-varying analytical solution of anisotropic visco-elastic tunnel excavation are presented through the correspondence principle.The anisotropic stress state means that the lateral earth press coefficient does not equal to 1 in this paper.A variety of ingredients on the displacement of surrounding rock are discussed.The results show that when the anisotropic parameter K0>1,the summit of tunnel will move in the direction of surrounding rock and then change to the opposite direction due to the rheological effect.However,the displacement will generate in the direction of inner tunnel when K0≤1,and the time-varying displacement gradually increases with the decreasing of K0.For the midpoint of the tunnel,the influence of the anisotropic parameter is just opposite to the summit displacement of tunnel.Moreover,the time-varying displacement of surrounding rock would increase with the increase of excavation speed and acceleration.The shear modulus and viscosity also have some influences on the time-varying displacement of surrounding rock.