AbstractTemporal growth of the h‐index in a diachronous cumulative time series is predicted to be linear by Hirsch (2005), whereas other models predict a concave increase. Actual data generally yield a linear growth or S‐shaped growth. We study the h‐index's growth in computer simulations of the publication‐citation process. In most simulations the h‐index grows linearly in time. Only occasionally does an S‐shape occur, while in our simulations a concave increase is very rare. The latter is often signalled by the occurrence of plateaus—periods of h‐index stagnation. Several parameters and their influence on the h‐index's growth are determined and discussed.