The method of extended cultivation was studied mathematical-analytical by a simple mathematical model. It was reflected on the control algorithm of feeding rate. Because corresponding to the model the substrate is consumed only for the biomass growth, the feeding is to control proportional to the biomass variation. It is shown that the biomass concentration in this case is independent of outflow and approaches a limit value. Relations between biomass growth and feeding rate of limiting substrate are given for all cases. In particular for the cyclie fed batch, it is shown that assuming periodic cycles the cultivation volume at the end of the cycles approaches a maximum value defined only by initial volume, specific growth rate and cycle period.