Leak detection is one of the most important problems in the oil and gas pipelines. Where it can lead to financial losses, severe human and environmental impacts. Acoustic emission test is a new technique for leak detection. Leakage in high pressure pipes creates stress waves resulting from localized loss of energy. Stress waves are transmitted through the pipe wall which will be recorded by using acoustic sensor or accelerometer installed on the pipe wall. Knowledge of how the pipe wall vibrates by acoustic emission resulting from leakage is a key parameter for leak detection and location. In this paper, modeling of pipe vibration caused by acoustic emission generated by escaping of fluid has been done. Donnells non linear theory for cylindrical shell is used to deriving of motion equation and simply supported boundary condition is considered. By using Galerkin method, the motion equation has been solved and a system of non linear equations with 6 degrees of freedom is obtained. To solve these equations, ODE tool of MATLAB software and Rung-Kuta numerical method is used and pipe wall radial displacement is obtained. For verification of this theory, acoustic emission test with continues leak source has been done. Vibration of wall pipe was recorded by using acoustic emission sensors. For better analysis, Fast Fourier Transform (FFT) was taken from theoretical and experimental results. By comparing the results, it is found that the range of frequencies which carried the most amount of energy is same which expresses the affectivity of the model.