A back analytical method for the excavation of a circular or elliptical tunnel in viscoelastic medium under in-plane and out-of-plane loadings at infinity is derived by using the theory of linear elasticity and the correspondence principle. The time-dependent behavior of rock masses with initial displacements is assumed to be represented by Standard model of viscoelasticity. The practical usefulness of the consideration of initial displacements and the back analysis is shown by several graphical representations and by the numerical results applied to some virtual measurment data.