Thermo-acoustic refrigerator constitutes a viable alternative to the search for suitable replacement of conventional refrigeration systems. Although the device is simple to build and environmentally friendly, the issue related to its efficiency requires some investigation. Advanced optimization schemes are being developed in order to handle the designing of the device which appears to be challenging with regards to the interdependence of its design parameters. In this paper, a mathematical programming formulation is presented in order to model and optimize the geometry of a simple standing-wave thermo-acoustic refrigerator. The model developed has been implemented in the software GAMS. The geometry of the stack, described as the heart of the device, constitute the focus of this study. The stack length and the stack position are the main variables considered in this work. This work provides guidance on the selection of the most suitable geometry of the stack in order for the device to achieve a relatively higher performance. In addition, the details of the mathematical programming model have been disclosed for further analysis and improvement.