A cell subjected to radiation damage could survive if the radiation induced lesions are repaired correctly or survive as a mutant if repaired incorrectly or die which is reflected by its inability to divide. In this paper we develop a stochastic model to analyse the effects of radiation on living cells incorporating the rates of lesion induction, damaged DNA replication and rates of repair, misrepair and death. The cell survival probability is explicitly obtained and is shown to be a concave function of the dose so that the obtained cell survival probability exhibits a “shoulder”. Also the number distribution of the potential lethal lesions which forms the core of cell studies is obtained. A brief comparison with other existing models has also been made. In particular, well known models of Neyman and Puri (1981) and Yang and Swenberg (1991) are obtained from our model and our results are in agreement with theirs. A linear-quadratic approximations for the cell survival probability as a function of dose is made. The model is shown to give sufficiently good fit for the survival data of EAT and CHO cells irradiated with different doses of UV-radiation and x-rays (Iliakis and Nusse (1982), Metting et. al. (1985))