This paper describes the free vibration analysis of a rectangular duct by using the Rayleigh-Ritz method. Static beam functions are used as admissible functions in the Rayleigh-Ritz method. These basis functions are the static solutions of a point-supported beam under a series of sinusoidal loads. The unique advantage of using this method is that it allows for the consideration of different axial boundary conditions of a duct. Computational results are validated with existing literature data for a simply supported rectangular duct and the finite element method (FEM) for other axial boundary conditions. A validated analytical model is used for generating natural frequency data for different dimensions of rectangular ducts. Further curve fitting has been done for the generated data, and an empirical relation has been presented to calculate the first fundamental natural frequency for different material properties of ducts and different axial boundary conditions, which can be used for any dimensions of the duct within the specified range. © 2015, International Institute of Acoustics and Vibrations. All rights reserved.