Intensification of technological processes along with increasing requirements for the accuracy of operations makes new demands on transmissions of machine units. It is especially important, in the mode of combating the negative influence of oscillatory processes, to ensure the smallest angle of misalignment between sections of shaft lines, especially for transmissions of high-precision machines with numerical program control. Known methods for reducing the negative effects of oscillatory processes are associated with the use of elastic couplings with low-rigidity metal elastic elements between shaft line sections. In most cases, the use of these devices is the main cause of the above problem in the form of significant angular misalignment of transmission shaft line sections. The paper presents the results of studies on the synthesis of structural diagrams of elastic couplings using metal elastic elements of low rigidity, but having a small twist angle of the half-couplings and complete preservation of their elastic functional capabilities. The research was conducted using a methodology based on the application of modified kinematic graphs in solving the analysis and synthesis of mechanical structures. As a result, new, theoretically substantiated solutions for structural diagrams of such couplings were proposed, which determines the creation of new real designs. The presented solutions are a generalization and selection of the best from a variety of different multi-variant solutions, which are different combinations of embedding additional mechanical structures in the form of planetary, friction or ordinary gear transmissions into the structure of the elastic coupling. It is proposed to use the results of the obtained solutions in relation to some existing designs of couplings with metal elastic elements of low rigidity in order to modify them to improve the functional capabilities.