We propose a numerical approximation to Buxton's general kinetic model (GKM) for ASL quantification that will enable greater flexibility in ASL acquisition methods. The proposed method combines the Bloch-McConnell equations with the flow effects and hence model the effects of flow simultaneously with magnetization transfer, T2 effects, off-resonance, and irregular timing of labeling. These can be solved using Jaynes’ matrix formalism. The proposed approximation is compared with GKM using simulations for PASL, PCASL, steady-pulse ASL, and MR fingerprinting ASL. Accuracy of the approximation is studied as a function of a key “time interval” parameter using Monte-Carlo simulations.