The theory of finite time thermodynamics is applied to analyze and optimize the performance of a thermoelectric refrigerator, which is composed of multi-elements. For the fixed total heat transfer surface area of two heat exchangers, the ratio of the heat transfer surface area of the high temperature side heat exchanger to the total heat transfer surface area of the heat exchangers is optimized for maximizing the cooling load and the coefficient of performance of the thermoelectric refrigerator. The effects of various parameters on the optimum performance are analyzed. The results may provide guides for the analysis and optimization of practical thermoelectric refrigerators. (C) 2003 Elsevier Ltd. All rights reserved.