In this work, a typical thermoacoustically driven pulse tube cooler as a no-moving part device has been investigated by a numerical method. A standing wave thermoacoustic engine as a prime mover in coupled with an inertance tube pulse tube cryocooler has been modeled. Nonlinear equations of unsteady one-dimensional compressible flow have been solved by the finite volume method. The model presents an important step towards the development of nonlinear simulation tools for the high amplitude thermoacoustic systems that are needed for practical use. The results of the computations show that the self-excited oscillations are well accompanied by the increasing of the pressure amplitude. The necessity of implementation of a nonlinear model to investigate such devices has been proven. The effect of APAT length as an amplifier coupler on the performance of the cooler has been investigated. Furthermore, by using Lagrangian approach, thermodynamic cycle of gas parcels has been attained. (C) 2014 Elsevier Ltd. All rights reserved.