In a standing wave thermoacoustic refrigerator, heat transport from the “cold” to the “ambient” end of a stack is achieved by means of an oscillatory motion of a compressible fluid undergoing cyclic compression and expansion. However, the stacks can be both costly and impractical to fabricate due to material and assembly costs, which limits the cost benefits of thermoacoustic systems. Some of these problems could be solved by the application of stacks that have irregular geometries, for instance stacks made of “random” materials from metal machining (swarf), which are often considered as waste. In this paper, the thermal performance of stacks made of a few selected materials is determined by carrying out experiments in a standing wave thermoacoustic refrigerator. The reported results will be beneficial for developing low-cost thermoacoustic refrigerators or heat pumps for both domestic and commercial applications.