Abstract: As a type of circumferential yielding supports, liner embedded with highly deformable elements can achieve the release of rock deformations through the compressible deformation of highly deformable elements. The paper aims to investigate the interaction mechanism between surrounding rock and liner with highly deformable elements. In this paper, the improved fractional Burgers model is established to describe the time-dependent behavior of rock, and then the analytical solutions for tunnel displacement and support pressure are derived taking into account the tunnel face advancement effect and the installation delay of support. In addition, the reliability and effectiveness of analytical solutions are well validated by comparing the monitoring data in Lyon-Torino Base tunnel. Furthermore, based on the analytical solutions proposed in this paper, a comprehensive parametric investigation including the influences of fractional order of rock constitutive model, supporting time and yield stress of highly deformable elements is carried out. The main conclusions are made as follows: The deforming ability of surrounding rock becomes stronger as fractional order of Burgers model increases, and the tunnel displacement and support pressure also exhibit an increasing trend; Supporting time has a great influence on tunnel performance. On the one hand, in order to keep rock stability it is recommended to install support structures as early as possible. On the other hand, the optimal number and length of highly deformable elements should be determined for ensuring that the support pressure varies within a range of bearing capacity of liner; The yield stress of highly deformable elements does not pose a significant effect on tunnel displacement and support pressure. However, this does not mean the yield stress of highly deformable elements can be determined randomly. There should be an appropriate range for this yield stress, where the purposes for both the tunnel stability and the release of rock deformation can be achieved.