The incorporation of epistemic and aleatory uncertainties for earthquake-induced risk assessment of Eccentric Braced Frames (EBFs) is of importance due to their contribution to the amount of damages and losses. Estimation of seismic structural responses taking uncertainties into account for EBFs requires a robust analytical model. Seven implicit behavioral parameters have been defined for shear links in EBFs all of which having specific Coefficient of Variations (COV) to define their behaviour under dynamic loadings. By using these parameters and several seismic records for Nonlinear Time History Analyses (NTHAs), the epistemic and aleatory uncertainties could be incorporated into the structural responses. The main goal of this paper is to estimate the median spectral acceleration (Samed) of EBFs as well as their dispersion corresponding to exceeding different performance levels using sampling-based reliability approaches and various Machine Learning methods (MLs) while trying to create a balance between the accuracy of the responses and required computational efforts. A 4-story EBF is considered and Correlation Latin Hypercube Sampling (CLHS) along with Incremental Dynamic Analysis (IDA) and Endurance Time (ET) method as NTHAs are used for propagation of epistemic and aleatory uncertainties. Then, in the next step, the Design of Experiments (DOE) is used to decrease time cost by considering only the most important interactions between behavioral parameters for determining median spectral acceleration as well as dispersion. Different ANNs including Support Vector Machines (SVMs) as well as Radial Bases Function Networks (RBFs) are trained and tested. The results obtained via ANNs are compared with CLHS to measure the accuracy and goodness of ANNs for predicting the median spectral acceleration. The results illustrate reasonable accuracy for determining seismic response using MLs.