Thermoacoustic refrigerators have huge potential to replace conventional refrigeration systems as an alternative clean refrigeration technology. These devices utilize conversion of acoustic power and heat energy to generate the desired cooling. The stack plays a pivotal role in the performance of Standing Wave Thermoacoustic Refrigerators (SWTARs), as the heat transfer takes place across it. Performance of stacks can be significantly improved by making an arrangement of different materials inside the stack, resulting in anisotropic thermal properties along the length. In the present numerical study, the effect of multi-layered stack on the refrigeration performance of a SWTAR has been evaluated in terms of temperature drop across the stack, acoustic power consumed and device Coefficient of Performance (COP). Two different aspects of multi-layered stack, namely, different material combinations and different lengths of stacked layers, have been investigated. The combinations of four stack materials and length ratios have been investigated. The numerical results showed that multi-layered stacks produce lower refrigeration temperatures, consume less energy and have higher COP value than their homogeneous counterparts. Among all the material combinations of multi-layered stack investigated, stacks composed of a material layer with low thermal conductivity at the ends, i.e., RVC, produced the best performance with an increase of 26.14% in temperature drop value, reduction in the acoustic power consumption by 4.55% and COP enhancement of 5.12%. The results also showed that, for a constant overall length, an increase in length of side stacked material layer results in an increase in values of both temperature drop and COP.