A new method is proposed for the analytical calculation of resonance integrals. Resonance integrals of infinite cylindric fuel cells are calculated according to a very simple analytical method with a reasonable level of accuracy. An escape probability based on a rational approximation is used to represent the neutron transport among the cell regions. The expression obtained for the resonance integral is a function of the temperature, geometry, and fuel rod composition, as well as the neutron energy. The terms of the expression are combinations of the well-known function J(ξ,β) and its partial derivatives in β. The formulation can be used for all resonance types (narrow, intermediate, and wide). The method parameters depend on the resonance type and can be obtained as a function of a single parameter. For this parameter, a simple expression dependent on the resonance parameters is proposed.