During the long-term operation of tunnels, surrounding rock undergoes creep effects under environmental loads, resulting in changes in the aging evolution model of stress and deformation in surrounding rock and lining, which affects the long-term operational safety of the tunnel. Therefore, using the model test device for time-dependent characteristics of stress and deformation of weak surrounding rock and lining structure in operational tunnels, taking into account the influence of tunnel burial depth and lateral pressure coefficient of surrounding rock, a model test on time-dependent characteristics of stress and deformation in weak surrounding rock and lining structure was conducted, and the stress and deformation time-varying curves at key locations of surrounding rock and lining were obtained. The time characteristics of surrounding rock stress, the contact force between surrounding rock and lining, internal force, and displacement of lining structure were analyzed. Research findings indicate that the stress of surrounding rock, the internal force and displacement of lining structure, and the contact force between surrounding rock and lining all increase and tend to be stable over time under constant load. This implies that the stress and deformation of the surrounding rock and lining structure exhibit time-dependent changes. With changes in burial depth and lateral pressure coefficient, significant variations are observed in the various indicators of stress and deformation in the surrounding rock and lining structure, indicating both time-dependent and long-term characteristics in terms of stress and deformation. The research results provide basic data support for the study of the time-dependent characteristics of stress and deformation between weak surrounding rock and lining structures in operational tunnels and can provide theoretical and technical guidance for the long-term service status discrimination and disaster prevention and control of operational tunnels.