Abstract: Based on the variational principle, the Relative Mode Transfer Method (RMTM), that we previously proposed, is deduced again in the present paper, for solving the vibration problems of continuous systems with arbitrary piece-linear boundary conditions and nonlinear boundary conditions that can be transformed into piece-linear boundary conditions. The derivations in this paper and reference 10 are compared in order to verify the validity of the RMTM and its advantages are discussed. A cantilever with a stop at the end and excited by a uniform distributed force is considered and the responses are obtained both by the RMTM and the Force Integration Method(FIM). The nonlinear vibration of the typical system is studied through the bifurcation response and the time history at the end, and the results are discussed.