Abstract This paper presents a brief review of previous developments in substructure synthesis methods using frequency response functions and proposes a new coupling analysis approach which takes into account the effect of elastic media between substructures—the so-called general joint description method (GJDM). The theoretical basis of the new method is presented here and applications are demonstrated via two numerical simulations. The elastic media between substructures, i.e., the joints, are described by general impedance matrices which have only boundary degrees of freedom. The introduction of elastic media into coupling analyses can reduce errors caused by improper treatment of joints in conventional coupling analysis methods and can also provide a solution for non-conforming interfaces, where the numbers of degrees of freedom at the interfaces of two substructures are not consistent. In addition, the new method enables the dynamic behaviour of an assembled structure be easily tuned by changing the joint parameters only. These advantages show that the GJDM is an efficient and versatile tool in substructure synthesis analyses.