Purpose <p>Boundary conditions of linear formulations are often used to solve nonlinear vibration equations. This paper studies the high-order vibration frequencies of a cantilever beam with corresponding nonlinear boundary conditions.</p> Methods <p>Using a trial function from the linear vibration analysis but different eigenvalues with nonlinear considerations, and integrating the nonlinear vibration equation over the length of the beam, vibration frequencies are obtained from the nonlinear governing equation, and the relationship between vibration frequencies and amplitudes of the cantilever beam is obtained.</p> Results <p>With this novel procedure and the linear mode-shape functions, numerical results show a close agreement with earlier studies from different solution techniques, particularly accurate at smaller amplitudes. The solution technique in this study, the subdomain method, is based on the utilization of integration over the physical domain after the robust Galerkin method is not applicable due to the extreme difficulty in evaluating the integrations involved.</p> Conclusion <p>The method and procedure offer an alternative technique for special nonlinear problems by combining linear solutions with the approximate algorithm.</p>