This thesis uses an energy-based approach to develop new analytical solutions for the time-dependent creep response of deeply embedded cavities. The new models developed here can be used for the initial design of tunnels and for other applications such as underground storage caverns and problems outside the field of geomechanics. The objective of using this energy-based approach is to develop models that can provide a quick estimate of cavity closure and that can be applied to different design situations and material behaviour. For the first time a three-dimensional analytical solution has been developed for the time-dependent response of a cavity embedded in a viscoelastic medium. The cavity is excavated quasi-instantaneously from an infinite body with an initial isotropic stress field. The problem is three-dimensional due to the effect of a tunnel face. This new solution can predict the full interaction between the tunnel and the surrounding creeping rock and thus can be incorporated with field monitoring data in an expert system for tunnel design. The accuracy of this model is comparable with finite element analysis. A new class of thermodynamically consistent constitutive models have been developed, which couple viscoplasticity and damage, describing both the secondary and tertiary stages of creep behaviour. Models were derived for both frictionless and frictional materials within the framework of hyperplasticity. The frictional model provided a good fit to data obtained from the triaxial compression testing of sandstone, illustrating its capability of describing creeping rock. These new constitutive models were incorporated into the energy-based method for cavity analysis, using a two-dimensional plane strain cylindrical cavity for demonstration purposes. A parametric study was carried out and results were also compared with FE analysis. Findings show that the models successfully describe the secondary and tertiary stages of creep behaviour. These new solutions only require a simple text file as an input and need minimal skill to operate. The formation of an initial geometry or finite element mesh is not necessary. This is shown through the creation of a standalone program for the three-dimensional model. The new solutions can take into account a wide range of different material behaviour, both two-dimensional and three-dimensional problems and due to their thermodynamic consistency are able to simulate other time-dependent processes, such as relaxation. This shows the flexibility of this approach and its applicability to different geomechanics problems.