A comprehensive entirely mechanistic model of the kinetics of cell population in vitro exposed to continuous irradiation is formulated and analysed. The model provides a stochastic description of the processes of formation and repair of radiation-induced lesions, as well as of cell cycling, cell proliferation, and cell death. Unobservable kinetic parameters of the model are estimated from experimental data on the sizes of clones formed in synchronized cultures of S3 HeLa cells exposed to continuous irradiation by gamma-rays at various dose rates. The effects of dose rate on cell cycle duration and damage repair kinetics are studied. Continuous and acute exposures with the same total dose are compared in terms of their impact on cell survival.