Tunnelling through the Himalayan geology presents significant challenges due to the poor quality rock mass and substantial overburden. The construction process encounters difficulties such as large deformations, squeezing, and the risk of block failure, often impeding the tunnelling operations. Consequently, understanding the stress–strain behaviour of the surrounding rock mass is crucial during the design phase of underground cavities and their support systems. This study introduces a novel numerical approach called the ‘Three-Stage Analysis Method’ for finite element analysis of tunnel-support interaction in squeezing ground under biaxial in-situ stresses. This method comprises three interconnected models in series representing various tunnel construction stages, including the sequence of tunnel excavation and convergence resulting from construction delays. The rock mass’s response, characterized by elastic-strain softening, is simulated using the generalized Hoek–Brown criterion coupled with a return mapping technique. Additionally, the tunnel support system is modelled to exhibit nonlinear behaviour. The Sawra-Kuddu Hydro-electric Project in India serves as a case study for investigating this framework. The interaction between the tunnel and support structures is quantified through parameters like tunnel convergence, principal stress distribution, ground-reaction-curves, and support-characteristic-curves. The study includes a comparison of the ground-reaction curves obtained with those from existing literature, highlighting the efficacy and unique insights provided by the proposed methodology. This research contributes valuable insights into the complex behaviour of tunnel-support systems in challenging geological conditions, enhancing the understanding and management of such projects.