We study the dynamics of classical correlation and quantum discord of two coupled two-level atoms interacting with a cavity initially in vacuum, coherent and thermal equilibrium states, respectively. The interplay between the atom-atom coupling and mean number of photons is considered. We find that, for a cavity in a vacuum state, classical correlation or quantum discord shows a sudden change in behaviour during the evolution, and evolves periodically for zero and very large qubit-qubit couplings. However, for coherent and thermal equilibrium s...