A dynamic analysis of an L-shaped structure by Rayleigh-Ritz substructure synthesis method (RRMSSM) was studied. The purpose of this study was to obtain an accurate eigensolution of an L-shaped structure. Two beams were modeled as uniform Euler-Bernoulli members of different physical properties. It was observed that for the lower frequencies, both approximate methods result in exact frequencies. As the approximate solutions start to differ slightly from the exact ones for higher frequencies, the 12-DOF RRMSSM proves to be more accurate than the 60-DOF FEM. The L-shaped structure does result in a highly accurate eigensolution based on low-order and linear eigenvalue problems. The application of RRMSSM for the first solution is more difficult to obtain but its accuracy is superior, and the second is based on the solution of high-order eigenvalue problems but it does not require the solution of a complex nonlinear transcendental equation.