A one-dimensional model of harmonic oscillations of a junction of several thin elastic rods has been developed. In contrast to the classical model of a single rod, the constructed model of the junction is not purely differential but includes new algebraic unknowns and algebraic equations evoked by the so-called readily movable elements of the structure. The asymptotic representations have been found for frequencies and natural modes of the elastic body oscillations and estimates of asymptotic residues have been obtained.