The aim of the present work is to analyze the sensibility of an elastic coupling on the coupled Frequency Response Functions (FRFs) of transmission mechanical systems. The FRF of a linked system, such as a reducer stage, is determined by a receptance coupling (RC) method. The equilibrium and the compatibility conditions are applied.This method is investigated for different coupling models such as rigid and flexible. The proposed method is validated by a direct computation of the full system showing exact agreement.Afterward, the effect of a rigid and a joined system on the sub-structuring response FRFs is analyzed. The coupling models derived from literature review are discussed to show their effects on FRF. Although the coupling in question is considered to be a flexible interface in the aforementioned system, as revealed in the literature review, it introduces a translational and rotational damping and stiffness. So, the formulation of the RC is different from the standard approach. In order to achieve the aim of the present work, the effects of some important parameters such as translational and rotational coupling, shaft and bearing stiffness on the FRF are discussed. Some sensitivity of the proposed models are observed in relation to the coupling parameters.