A strong stochastic component has been described for the appearance of senescent cells in cultures that have not completed their in vitro lifespan. The proliferative potential of individual clones show a bimodal distribution. Additionally, two cells arising from a single mitotic event can exhibit large differences in their doubling capacities. In this report we present a model and a computer simulation of the model that explains the observed stochastic phenomena. The model is based on both gradual and abrupt telomere shortening. Gradual telomere shortening (GTS) occurs during each cell division as a consequence of the inability of DNA polymerase to replicate the very ends of chromosomal DNA. It is responsible for the gradual decline in proliferative potential of a cell culture, but does not explain the stochastic aspects of cellular aging. Abrupt telomere shortening (ATS) occurs either through DNA recombination or nuclease digestion at the subtelomeric/telomeric border region of the chromosome. Recombination involves the invasion of a telomere single-strand three-prime protruding end at this border in the telomere of the same chromosome or in another subtelomeric/telomeric region. Shortening of one or more telomeres in the cell causes a sudden onset of cell senescence, referred to as sudden senescence syndrome (SSS). This is manifested as a stochastic and abrupt transition of cells from the larger to the smaller proliferative potential pool and can cause cell cycle arrest within one cell division. The computer simulation matches well with experimental data supporting the prediction that abrupt telomere shortening underlies the stochastic onset of cell senescence. Sudden senescence syndrome appears to be the most important mechanism in the control of the extent of proliferation of a cell culture because it prevents virtually every cell in the culture from reaching its maximum doubling capacity, that would otherwise be allowed by telomere shortening via the end-replication mechanism alone.