Structural steel plates having engineered cut-outs to exhibit controlled yielding is recently proposed for desirable performance compared to conventional systems. Butterfly-shaped beams with hexagonal cut-outs inside of the beam’s web is studied to better align the bending strength diagram along the link length with the corresponding demand shape of the applied moment diagram. In previous studies, it has been reported that these links have substantial energy dissipation capability and sufficient ductility which necessities further investigations. In this study, a set of 240 nonlinear finite element models are developed for creation of a database and subsequently calibrated with finite element software packages. The capability of the gene expression programming (GEP) is explored for prediction of force-displacement relationship of a butterfly-shaped beam. Two new models are developed based on the reliable generated database. Subsequently, the proposed models are validated with several conducted analysis and statistical parameters, for which the comparisons are shown in detail. The results represent that the proposed models are able to predict the force-displacement relationship of a butterfly-shaped beam with satisfactory accuracy.