Abstract: High-stress tunnel excavation is usually accompanied by the occurrence of surrounding rock rheology, which causes damage to the tunnel structure and threatens the safe operation of the tunnel. A time-dependent mechanical model of surrounding rock and support of deep buried tunnels was established, taking into account the coupled influence of the spatial effect of the excavation face and the rheological characteristics of the surrounding rock. Based on the Kelvin-Voigt model, the analytical solution for the deformation of the surrounding rock in the unsupported state and the analytical solutions for the displacement and support pressure of the tunnel after support were derived. The feasibility of the analytical solutions was verified by comparison with numerical simulation. Moreover, a sensitivity analysis was conducted on parameters such as tunnel excavation speed, rock stress release coefficient, and lining installation time. The results show that compared with the existing research, the calculation accuracy of the analytical solution of the radial displacement of the surrounding rock is increased by 10.2 % on average, and the calculation accuracy of the support pressure is increased by 8.2 % on average. The rock displacement without considering the spatial effect of the tunnel face is overestimated, while the support pressure is underestimated. The increase in tunnel excavation speed will increase rock tangential stress, and reduce the restraining effect of the support structure on the deformation of the surrounding rock. Rock stress release or the delay in lining installation time will lead to an increase in tunnel deformation and rock mass tangential stress, resulting in instability and failure of the surrounding rock, but it can also reduce the support pressure. The change in lining installation time has the most significant impact on the surrounding rock stress, displacement and support pressure, while the excavation speed has the least impact. In practical engineering, the influence of various factors should be comprehensively considered in order to achieve a balance and stability between the surrounding rock and the support.