Although many studies have been carried out for estimating the afflux through modern straight deck bridge constrictions, little attention has been given to medieval arched bridge constrictions. Hydraulic Research Wallingford in the UK (Brown, P.M., 1988. Afflux at arch bridges. Report SR 182. Wallingford, UK: HR Wallingford) recently published a major coverage of both experimental and field afflux data obtained from arched bridge constrictions. The report pointed out that the present day formulas developed for estimating the bridge afflux are inadequate to apply to ancient arched structures. Therefore, this study aimed at developing new afflux methods for arched bridge constrictions using multi-layer perceptrons (MLP) neural networks, radial basis function-based neural networks (RBNN), generalised regression neural networks (GRNN) and adaptive neuro-fuzzy inference system (ANFIS) model. Multiple linear and multiple nonlinear regression analyses were also used for comparison purposes. Mean square errors, mean absolute errors, mean absolute relative errors, average of individual ratios between predicted and actual values, and determination coefficients were used as comparison criteria for the evaluation of model performances. The test results showed that MLP, RBNN, GRNN, and ANFIS models gave reasonable accuracy when applied to both the field and experimental data collected by Hydraulic Research Wallingford.