Noise radiation from a flexible rectangular duct wall in a transverse direction involves a phenomenon of acoustic-structural coupling. Maximum sound radiation happens near coupling modes due to effective energy exchange between acoustic-structural subsystems. Prediction of the coupling modes and also understanding of dominant mode behavior in the flexible rectangular duct requires free vibration analysis. The present paper discusses the mode coupling approach and Impedance-Mobility formulation. Mode coupling approach is used to calculate the coupled natural frequency. Impedance-Mobility formulation is used to decide the dominant uncoupled mode type at the coupled frequencies. In the impedance-mobility approach, it is presumed that coupled response can be described in terms of finite sets of the uncoupled acoustic and structural modes of a duct. Impedance and Mobility terms are expressed in terms of uncoupled frequencies of acoustic and structural subsystems. Uncoupled duct structural modes are calculated by using the equivalent plate model. The calculated impedance and mobility matrices are arranged in the form of Eigenvalue problem to calculate the Eigen frequencies and decay time. The dominance of coupled behavior in a system can be estimated using transfer factor which developed based on the electrical transfer factor theory. This factor can be used as a computational criterion to decide the coupled or uncoupled analysis. Parametric studies are conducted to understand the effect of duct wall thickness and damping.