SummaryThis paper concerns the application of the constant deflection-contour method to problems involving nonlinear vibrations. Two specific problems are considered: a clamped circular plate and an annular plate with free inner boundary. For the linear case, the results obtained offer excellent agreement with previous studies, indicating significant potential for the utilization of this method in different nonlinear cases. The analysis may be applied to other types of geometrical structures. Notwithstanding the fact that only a first-term approximation has been made for the deflection function, in conjunction with the Galerkin procedure, excellent agreement has been found. Additional analytical calculations could be made to improve accuracy, indicating that the method could prove particularly useful when employed with a symbolic manipulation package.