A model for cell kinetics of human acute lymphoblastic leukemia has been constructed with discrete modeling techniques for computer use with the GPSS/360 computer language. The model has produced results corresponding to observed biological data. It has been possible to explore mechanisms for control of the growth of the leukemic cell population. In addition to the flow of cells from the resting to the proliferative phase, two other important parts of the cell life cycle, cell death and the intracellular events after mitosis, were identified as potentially important regulatory mechanisms. Chemotherapeutic drug effects could be simulated, and in the case of vincristine an unsuspected effect was suggested. This effect of vincristine on transformation of the resting cell to an active proliferative phase has been supported by studies of vincristine effect on blast transformation of phytohemagglutinin-stimulated lymphocytes. A single cell was found to take 3½ yr to grow to a population of 1012 cells, a clinically recognizable number. Although this observation cannot be confirmed from biological studies, this time has an interesting correspondence to the peak incidence of acute lymphoblastic leukemia in childhood. It indicates that a mutational event in a single cell could account for the leukemic process in childhood acute leukemia.