When the construction of tunnels encounters with the filled Karst cave, the instability of confining rocks normally causes the geological hazards like water or mud inrush. Based on the limit analysis theorem, a calculation method to investigate the stability of confining rocks was proposed. In view of latent filled karst cave existing in the circumferential direction of the tunnel, transformed strength parameters of Hoek-Brown nonlinear failure criterion were obtained by virtue of the generalized tangent technique, and the two-dimensional model was constructed as well. In order to characterize the stability of the confining rocks, safety factor was introduced into the energy dissipation analysis on the basis of upper bound theorem and strength reduction technique. The variations of safety factor with respect to the diverse parameters were then discussed through optimization analysis. The computed results show that the parameters, including thickness of rock plug, pressure in Karst cave, tunnel supporting pressure, diameter of the circular cross section, uniaxial compressive strength, and parameters of Hoek-Brown failure criterion had significant influence on the variations of safety factor. And it is found that the safety factor was insensitive to the change of unit weight of surrounding rock. Moreover, the proposed method was applied to engineering projects, and reasonable results were obtained, which verified the validity of the proposed method.