A mathematical model combining deterministic and stochastic elements describes the growth and division of single cells. Its deterministic part is based on the model of Baranyi and Roberts [International Journal of Food Microbiology 23 (1994) 277] modelling the gradual adjustment of the cells to a new environment. The stochastic part assumes a random threshold size for the division of a single cell, which accounts for the variability of the individual generation times. Experimental results of the first division times of thousands of single cells using a microscopic flow system could be reproduced with this model, and it has the potential to be used to study the effects of different stress and environmental factors on the distribution of the lag and generation times of individual cells.