Abstract: The combined effect of surrounding rock rheology and lining deterioration is the most critical factor affecting the long-term safety of deep buried soft rock tunnels in service. Based on a theoretical analytical method, this study first establishes a mechanical model of a tunnel under non-hydrostatic stress conditions. In this model, the Burgers viscoelastic constitutive law is used to describe the rheological behavior of the surrounding rock, and the deterioration of the mechanical properties of the lining concrete is characterized by the decay of its elastic modulus and strength over time. Secondly, time-dependent theoretical solutions for tunnel displacements and interface stresses are derived, providing analytical expressions that describe the long-term mechanical behavior of the tunnel. Furthermore, the reliability and feasibility of the proposed theoretical model are verified by degenerating the present solutions into existing simple cases and by comparing with numerical simulation results. Finally, systematic parametric analyses are conducted using the theoretical model to discuss the influence of surrounding rock rheology, lining deterioration, and ground stress conditions. The results show that there exists a threshold value for η_M (a parameter characterizing the long-term rheological rate of the surrounding rock). Only when η_M is below this threshold does its decrease induce a significant increase in radial displacement of the tunnel, as well as in radial and circumferential stresses at the interface; whereas the circumferential displacement and interfacial shear stress are not sensitive to the change in η_M. The larger the deterioration rate of concrete, the faster the tunnel displacement increases, and the more pronounced the decrease in interfacial stresses. There also exists a threshold for the deterioration rate. Beyond this value, the deterioration of concrete leads to intensified changes in tunnel displacement and interfacial stresses. The lateral pressure coefficient influences the distribution patterns of tunnel displacement and interfacial stresses, and there are significant differences in the mechanical response of the tunnel under hydrostatic versus non-hydrostatic stress fields. The theoretical model established in this study has superior applicability and can provide theoretical support for long-term safety assessment of tunnels in service.