The hypergeometric state is a one-parameter generalization of the binomial state. Itcan reduce to the binomial state in certain limit. The interaction of the binomial statewith two-level atoms in cavities has been studied in detail in the literature. In this article

we study the interaction of the hypergeometric state with two-level atoms. We usethe intensity-dependent Jaynes-Cummings model and the interaction is of intensity-dependent type. The dynamics of atomic population inversion and second order correlationfunction of the field were studied in detail. The collapse and revival phenomena arefound when the initial field state is the hypergeometric state. The field can show antibunching effects. The antibunching effect is better than that of the binomial state.