Significant advancements in developing earth-air heat exchanger models have been detected in the past several decades. It is worth mentioning that this type of device takes advantage of the Earth's constant temperature to cool or heat spaces in buildings so that the identification of its most appropriate geometric configurations to reduce energy consumption is still an actual challenge. In this context, the present paper is focused on the geometric evaluation of several earth-air heat exchangers arrangements according to the Constructal Design method. The performance indicators are the minimization of its soil volume occupation, the minimization of its airflow pressure drop, and the maximization of its thermal potential. Therefore, from a straight duct named Reference Installation, 26 complex geometries have been outlined here using the numerical-analytical investigation. Many ideas emerged from this study: the use of serpentine with low spacing between ducts reduced nearly 39% of the soil volume occupied by the device compared to Reference Installation, showing its applicability in urban regions. In addition, configurations with few curves benefited the decrease of air pressure drop, allowing a performance 30% superior to the most complex shapes. Instead, complex designs can be recommended for thermal potential increase, although the influence of the different configurations over this indicator was not substantial since the maximum improvement achieved between the best and worst shapes proved to be around 6%. Finally, when the three performance indicators are concomitantly considered, several complex geometries reached an overall performance superior to the Reference Installation.