In this paper, we develop a component mode synthesis method that relies on artificial springs to connect the subsystems of a built-up structure. The modal behaviour of the subsystems can be computed using different approaches, from analytical to numerical methods, depending on their complexity. The advantage of using artificial springs to link the subsystems is that one can model them with the Rayleigh–Ritz method, which is problematic in component mode synthesis. As known, the approximating functions must satisfy the system boundary conditions and the use of artificial springs avoids this difficulty. Moreover, and as in other component mode synthesis approaches, one can build reduced-order models at the subsystem level to significantly diminish the dimensions of the entire built-up structure, resulting in substantial reduction of the computational cost when performing numerical simulations. The method is first presented for the simple case of two axially connected beams. Two more complex cases are then addressed. The first one deals with two beams connected at right angles and the second one deals with an internal floor attached to a cylindrical shell, which reminds of some aeronautical structures. The performance of the method is carefully analysed and validated against finite element simulations.