<p>Vibrations play an extremely important role in most industrial branches, in transport, civil engineering, in multibody systems. Damping is a property that appears in these systems and determines, in a decisive way, good functioning. In this context, a proper modeling of the systems, which then provides a description of the phenomena that appear and the possibility of theoretical studies in the design phase is necessary in most engineering applications. Classical analysis methods for the study of damping use in the first instance viscoelastic models, which, however, provide approximate results, valid only under certain conditions. The Rayleigh damping model is more suitable but also presents quite limitations and sometimes provides results far from reality. The best method for systems with several degrees of freedom is the Caughey factorization which meets a series of advantages and proves useful in applications. The least squares approach is suggested in the paper as a way to build the damping matrix approximation. Thus, the benefits of modal decoupling can be applied to real-world computations.</p>