Access to inexpensive cooling sources is a precondition for developing cost-effective methods to mitigate heat stress among farm animal under hot climate conditions. The earth-air heat exchanger (EAHE) is a promising energy-effective technique that can be used to reduce the cooling load of a livestock building in hot days. Several studies have been carried out to assess the feasibility of EAHE for tempering air in livestock buildings. However, no mathematical model serving for EAHE design for livestock buildings has been developed, in which the EAHE system is often operated continuously to keep animals comfortable and productive. This work firstly deduced a regression model for predicting the air temperature difference between an EAHE tube inlet and outlet (ΔT_i-o) using response surface methodology (RSM) based on the data obtained from validated steady-state numerical simulations. Four key design and operation factors (tube diameter, tube length, air velocity, and the temperature difference between inlet air and the undisturbed soil) were incorporated into the model. Based on the regression model, a mathematical model for predicting the cooling capacity (CC) of an EAHE tube was obtained. Parametric analysis was conducted to reveal the effects of the four factors on both the ΔT_i-o and the CC. The models on cooling performance allow the designers to optimize the EAHE configuration for cooling livestock buildings.