The finite group invariance of theE⊗ &bgr; and Jaynes‐Cummings models are studied. A method is presented to obtain finite group invariance of theE⊗ &bgr; system.A suitable transformation of a Jaynes‐Cummings Hamiltonian leads to equivalence ofE⊗ &bgr; system. Then a general method is applied to obtain the solution of Jaynes‐Cummings Hamiltonian with Kerr nonlinearity. Number operator for this structure and the generators ofsu(2) algebra are used to find the eigenvalues of the Jaynes‐Cummings Hamiltonian for different states. By using the invariance of number operator the solution of modified Jaynes‐Cummings Hamiltonian is also discussed. © 2004 American Institute of Physics