An empirical acoustic impedance model of acoustic resonators with extended neck at a high sound pressure environment is proposed. The acoustic resonator with extended neck into its cavity is appropriate for the launcher fairing application because the length of neck does not increase the total height of the resonator. This enables one to design slim and light acoustic resonators for launch vehicles. The suggested acoustic impedance model considers the incident pressure and geometric variables(the neck length, the perforation ratio and the hole diameter) in terms of non-dimensional variables. Several acoustic resonators with extended neck are manufactured and their wall impedances are measured according to the pre-defined incident pressure levels. Effects of non-dimensional variables on the non-linear acoustic impedance are investigated so that a simple non-linear impedance model for the launcher fairing application can be proposed. It is demonstrated that the estimated acoustic resistance and acoustic length correction show reasonable agreement with the measured ones within the range of design parameters for launcher fairings.