The generalized lightning traveling current source return stroke model (also called GTCS model) represents generalization of all engineering lightning return stroke models that is generalization of the transmission line (TL models, also called current propagation models) and traveling current source models (TCS models, also known as current generation models). The channel discharge function was introduced and calculated for special cases within the GTCS model. We applied new numerical method for the calculation of the channel discharge function. The proposed method is highly accurate, extremely efficient and relatively simple.