A kinetic model is developed for the catalytic cracking of vacuum gas oil in terms of the elementary steps of carbocation chemistry. The composition of the hydrocarbon mixture is detailed up to the C-number. Next to the individual n-paraffins, the i-paraffins, n- and i-olefins, mono- di- tri-and tetra-naphthenes, the corresponding aromatics and the naphtheno-aromatics are lumped per C-number so that a link with modern analytical techniques is possible. Within each lump all likely chemical species are considered and accounted for in the network generation. The latter is performed by means of Boolean matrices and auxiliary vectors characterizing the molecules and carbocations. The kinetic modeling leads to the so-called single-event rate parameters which are invariants of the type of elementary steps they are related with. Some 50 single-event rate parameters were determined from an extensive experimental program on the catalytic cracking of key components with the relevant structures. The kinetic model was then inserted into a reactor model for the simulation of riser catalytic cracking. The results are represented in terms of the yields of 646 lumps or of the usual oil fractions, obtained from an interface post-processing the results generated at the elementary step level.