To investigate and predict the variation of groundwater dynamics in the Luohuiqu irrigation district of Shaanxi, different methods for researching the dynamics are assessed. Evaluation and prediction of groundwater levels via specific model(s) helps in forecasting of groundwater resources. Among different robust tools available, Support Vector Machines (SVM) and Back-Propagation Artificial Neural Network (BPANN) models are commonly used to empirically forecast groundwater dynamics. The Support Vector Machine is an increasingly popular learning procedure that is based on statistical learning theory. It involves a training phase, in which the model is trained by a training dataset of associated input and target output values. The Back-Propagation Artificial Neural Network is widely used and effective, because of its flexibility and adaptability in modeling a wide spectrum of problems. In the network, data are fed forward into the network without feedback, and all links between neurons are unidirectional. These networks are versatile and can be used for data modeling, classification, forecasting, control, data and image compression, plus pattern recognition. The SVM and BPANN models are proposed for predicting groundwater dynamics and building a predictive model. The two corresponding computer programs are compiled by the MATLAB program. Here, we discuss the modeling process and accuracy of the two methods in the assessment of their relative advantages and disadvantages, based on Absolute Error (ABE), Relative Error (RE), Maximum Error (ME), Average Error (AVE) and coefficient of efficiency (CE). Based on several years of measured irrigation data, relative advantages and disadvantages of the two models for predicting groundwater dynamics are compared. The results show that both SVM and BPANN have sufficiently high accuracy in reproducing (fitting) groundwater levels, and the CE for both is 0.99 in the study phase. However, in the validation phase, comparison of predictive accuracies of the SVM and BPANN models indicates that the former is superior to the latter in forecasting groundwater-level time series, in terms of ABE, RE, ME and AVE. The comparison also indicates that the SVM approach was more accurate in forecasting groundwater levels. Thus, the study results suggest that the SVM model is more reliable than BPANN for predictive modeling of groundwater levels. Although SVM shows great superiority in predicting and simulating groundwater levels, it should be recognized that it has many limitations. For instance, prediction and simulation accuracy depends greatly on the quantity and quality of the training set. Therefore, it is necessary to periodically retrain the SVM with new data. This is not only because of temporal evolution of the physical process, but also because of the necessity of a complex, diverse and more extensive training set for attainment of better prediction results. The SVM model expresses well the complicated coupling relationship of groundwater dynamics, and is more suitable for SVM prediction. Therefore, application of this method to such prediction within the irrigation district is feasible and practical. It is also complementary and ideal for traditional research methods of groundwater dynamics. Consequently, we recommend the SVM approach for these applications, based on the supporting evidence presented here.