The mechanical response of complex elastic structures that are assembled of substructures is significantly influenced by joints such as bolted joints, spot-welded seams, adhesive-glued joints, and others. In this respect,computational techniques, which are based on the direct finite element method or on classical modal reduction procedures, unfortunately show an inefficient balance between computation time and accuracy. In the present paper, a novel reduction method for the physical (nodal) joint interface degrees of freedom is presented, which we call joint interface modes. For the computation of the joint interface modes, Newton’s third law (principle of equivalence of forces) across the joint is explicitly accounted for the mode generation. This leads to a dimension of the generalized joint interface degrees of freedom in the reduced system, which is a factor of 2 or more smaller than in conventional reduction methods, which do not consider Newton’s third law. Two different approaches for the computation of the joint interface modes are presented. Numerical studies with bolted joints of different complexities are performed using a simple but representative constitutive joint model. It is demonstrated that the new joint-interface-mode formulation leads to both excellent accuracy and high computational efficiency.