Abstract: Large deformation problem in soft rocks tunnels at great depth has become a great challenging task for many rock engineers. According to the deformation characteristics of soft rocks under high pressure, yielding supports following the principle of deformation release are able to accommodate rock deformations without being damaged, having been proved to be a feasible and effective solution to deal with such problem. The main purpose of this paper is to theoretically investigate the mechanical response of a deep circular tunnel excavated in rheological rock masses, where yielding supports are applied. Based on the fractional derivative theory the improved fractional Burgers creep model by adopting the Abel viscous element is established to describe the time-dependent deformations of geomaterials. In addition, the correction coefficients of supporting stiffness in different deformation stages are proposed aiming at solving the problem that the traditional supports are unable to take the rock deformation release into account. According to those, this paper derives the analytical solutions for stresses and displacements around the tunnel in different deformation stages, considering the installation delay of support structures. Furthermore, in order to validate the effectiveness and reliability of the theoretical analyses, a well agreement between different solutions and field results can be obtained. Finally, the parametric investigation demonstrates that tunnel displacement and support pressure are greatly influenced by the fractional order of Burgers model representing the deformability of rocks. There exists a linear relationship between tunnel displacement or support pressure and yielding displacement. This linear relationship can also be found between tunnel displacement or support pressure and the correction coefficient of support stiffness. If this correction coefficient ranges in a low level, the change of tunnel displacement or support pressure is not remarkable. This paper may provide a new trail to quickly evaluate the time-dependent deformations of tunnels with yielding supports.