High-pressure tunnels with reinforced concrete lining have been extensively utilized in project practice. This study aims at developing a complete hydro-mechanical numerical model of high-pressure tunnels with emphasis on the interaction between lining and rock mass. In the model, a fully hydro-mechanical coupled formulation for saturated porous media is first established. A virtual element approach is proposed and combined with the master–slave contact algorithm to consider the interaction between lining and rock mass under hydro-mechanical coupling. A simple elastic-damage model is proposed to model the mechanical behaviour of the reinforced concrete lining. Moreover, the evolution formulations of the cracking and permeability of the reinforced concrete lining are derived based on China’s specifications. The proposed numerical model is first verified by simulating two examples that have analytical solutions. Then, the case study of an actual high-pressure tunnel is carried out. The whole water infilling process is numerically simulated and the obtained results are compared with the measured field data. The consistence between them further verifies the present numerical model. Consequently, some primary design-related parameters are investigated numerically with the present numerical model, and the results can be considered as general guide rules for the design of high-pressure tunnels.