An undular hydraulic jump on a smooth boundary occurs when the approaching flow Froude number marginally exceeds its critical value of unity. The free surface profiles of undular hydraulic jumps are studied theoretically by using the steady-state flow equation. It is established that the undular hydraulic jump phenomenon takes place because of the instability of the flow and can be described by the instability principle. The threshold of an undular hydraulic jump can be represented by a monotonic increasing curve of approaching flow Froude number versus boundary inclination. The elevation of the undular free surface increases with an increase in boundary inclination, but the amplitude of the free surface waves decreases with downstream distance. The theoretical results are well comparable with the experimental data. © 2012 American Society of Civil Engineers.