In this study

analytical viscoelastic solutions were derived for the lined circular tunnels by the correspondence principle and complex variable method under full contact and smooth contact conditions between liner and ground in non-hydrostatic stress field. In the solutions

all kinds of viscoelastic tunnels with an elastic liner was considered and the delayed installation of the liner was also taken into account. Therefore

the obtained analytical solutions can be applied to all linear viscoelastic models. The analytical solutions were verified by the solutions of references and numerical results. According to the solution

the surrounding rock was assumed to conform to the generalized Kelvin (H-K) viscoelastic body. The results showed that the radial

tangential stress

the circumferential displacement of the lining and the bending moment of the lining increased with time until converged to the fixed value. Under two kinds of contact conditions

there were quite differences on the displacement of the surrounding rock

the stress distribution of the lining

the distribution of the displacement and the internal force. Furthermore

the above differences between these two conditions increased with the time. Compared with the existing solutions

the solutions derived in this paper are more suitable and reasonable for practical deep buried tunnels especially for the full contact condition. The comparison between the two solutions can provide a useful reference for selecting liner and construction reasonably.