The standing wave thermoacoustic refrigerator, which uses sound generation to transfer heat, was developed rapidly during the past four decades. It was regarded as a new, promising and environmentally benign alternative to conventional compression vapor refrigerators, although it was not competitive regarding the coefficient of performance (COP) yet. Thus the aim of this paper is to enhance thermoacoustic refrigerator’s stack performance through optimization. A computational optimization procedure of thermoacoustic stack design was fully developed. The procedure was designed to achieve optimal coefficient of performance based on most of the design and operating parameters. Cooling load and acoustic power governing equations were set assuming the linear thermoacoustic theory. Lagrange multipliers method was used as an optimization technique tool to solve the governing equations. Numerical analyses results of the developed design procedure are presented. The results showed that the stack design parameters are the most significant parameters for the optimal overall performance. The coefficient of performance obtained increases by about 48.8% from the published experimental optimization methods. The results are in good agreement with past established studies.