When a water-rich karst cavity exists in front of the tunnel face, the thickness of the anti-inrushing rock mass between the tunnel face and the water-rich karst cavity will gradually decrease as the excavation of the tunnel progresses. Once the thickness of the anti-inrushing rock mass reaches the limit, the water inrush disaster will occur. An accurate prediction of the minimum safe thickness of the anti-inrushing structure can effectively avoid the occurrence of water inrush disaster in karst area. For the shear failure and bending failure modes of the anti-inrushing structure caused by water pressure, the corresponding mechanical models of anti-inrushing structure are established. The minimum safe thicknesses of anti-inrushing structure for the two models are calculated by using the shear strength criteria, the bending strength criteria, and the elastic thin-plate theory. The results calculated by present models are in good agreement with those calculated on the basis of the bending theory of fixed beam, the shear theory of rock column, and catastrophe theory. The results of parameter sensitivity analysis show that: 1) The water-insulating rock mass of deep-buried tunnel is prone to the bending failure, and the water-insulating rock mass of shallow tunnel is prone to the shear failure. 2) The minimum safe thickness of anti-inrushing structure is positively correlated with tunnel excavation radius, karst water pressure and Poisson’s ratio, and the order of influence degree from large to small is tunnel excavation radius, karst water pressure and Poisson’s ratio of surrounding rock. 3) The boundary conditions of the model will affect the minimum safe thickness of the anti-inrushing structure. When the excavation radius R<6 m and the karst water pressure Pw<0.35 MPa, the minimum safe thickness can be calculated based on the boundary simply supported condition. When R≥6 m and Pw≥0.35 MPa, the minimum safe thickness need to be calculated based on the fixed boundary conditions. This method provides a new way for the calculation of water gushing of circular tunnel in water-rich karst area. Finally, combined with a karst tunnel with water inrush, the corresponding parameters are substituted into the bending type Ⅰ expression, and the minimum safe thickness is generally consistent with the thickness reserved in the project, which shows that the analytical solution of the minimum safe thickness in this paper is reasonable.