Abstract: For the rheological rock with time-dependent behaviors, the mechanical response is greatly affected by the sequential construction of the tunnel. The cross-section excavation, longitudinal advancement, rockbolt reinforcement and liner installation are accounted for during the analytical derivation for a deeply buried circular tunnel in viscoelastic rock. The characteristics of rockbolt reinforcement region are regarded as homogeneous cylindrically anisotropic elasticity, and the corresponding method is then proposed. Accounting for the whole construction process, including sequential excavation, reinforcement and liner installation, the closed form solutions are derived when the rock is simulated to Burgers viscoelastic model. Based on the solutions, an extensive parametric analysis is then performed to investigate the influences of anisotropy degree, installation time of rockbolt and liner and thickness of reinforced region on tunnel convergence and the stresses. The analysis shows that the hoop stiffness of the reinforced region has a significant impact on the mechanical response of rock, while the effect of radial stiffness is much less. The stresses of the liner are greatly affected by its installation time, and the installation time of the rockbolt has no effect on the stresses. Increasing the thickness of reinforced region can reduce the convergence and optimize the stresses of reinforcement region, but it has little effect on the stresses of the liner. The proposed solutions can be applied to the preliminary design of tunnel construction with similar conditions.