Abstract Evapotranspiration is an important component in planning and management of water resources. It depends on climatic factors and the influence of these factors on each other makes evapotranspiration estimation difficult. This study attempts to explore the possibility of predicting this important component using three different heuristic methods: support vector machine (SVM), adaptive neuro-fuzzy inference system (ANFIS) and gene expression programming (GEP). In this regard, according to the Food and Agriculture Organization of the United Nations (FAO) Penman-Monteith equation, the monthly potential evapotranspiration in four synoptic stations (Zahedan, Zabol, Iranshahr, and Chabahar) was calculated using monthly weather data. The weather data were then used as inputs to the SVM, ANFIS and GEP models to estimate potential evapotranspiration. Five different input combinations were tried in the applications. The results of SVM, ANFIS and GEP models were compared based on the coefficient of determination (R2), mean absolute error and root mean square error. Findings showed that the SVM model, whose inputs are average air temperature, relative humidity, wind speed, and sunny hours of the current and one previous month, performed better than the other models for the Zahedan, Zabol, Iranshahr, and Chabahar stations. Comparison of the three heuristic methods indicated that in all stations, the SVM, GEP and ANFIS models took first, second, and third place in estimation of the monthly potential evapotranspiration, respectively.