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The generalized rotating-wave approximation (GRWA) is presented for thetwo-qubit and cavity coipling system . The analytical expressions in the zerothorder approximation recover the previous adiabatic ones. Thecounterrotating-wave terms can be eliminated by performing the first ordercorrections. An effective solvable Hamiltonian with the same form as theordinary RWA one are then obtained, giving a significantly accurate eigenvaluesand eigenstates. Energy levels in the present GRWA are in accordant with thenumerical exact diagonalization ones in the a wide range of coupling strength.The atomic population inversion in the GRWA is in quantitative agreement withthe numerical results for different detunings in the ultrastrong couplingregime.

Generalized rotating-wave approximation to the two-qubit and cavity coupling system