We introduce a compact model for characterizing the transient program operation of Gate-All-Around (GAA) Barrier-Engineered charge-trapping NAND flash (BE-CTNF) memory, especially in the FN-tunneling regime. Differing from prior models, our approach involves the calculation of threshold voltage shift attributed to each trapping layer, taking into account GAA structure of the cell and, at the same time, electron trapping within the oxide-nitride-oxide (ONO) tunneling layer. We validated our model through a comprehensive analysis of various physical parameters, with calibration to the results from the 3-D TCAD simulation.