It is believed that irradiation interacts with biological tissues to break or modify the DNA, which is the molecule contained in the nuclei of cells that carries all the relevant information for the organism. As such, radiation is dangerous for individuals; however, its properties can also be used in medicine, e. g. in cancer treatments. Nevertheless, the exact mechanisms of cellular response to radiation are not fully understood yet, especially for low doses (below 50 cGy), where non-targeted effects, i. e. that do not involve only the interactions radiation-DNA, are taking place. In order to deepen the knowledge of those non-targeted effects, a computer model of a population of cells irradiated in vitro was written, taking into account the phenomena in the low dose domain.As a start, two non-targeted effects were studied, the bystander effect and the low dose hyperradiosensitivity. The program was written in C++ and the technique of the cellular automaton was used. The clonogenic assay was reproduced; cells were seeded in a dish and if the colony they formed after a given period of time was bigger than 50 cells, the seeded cells were assumed to have survived. The direct effect of radiation was calculated by the traditional linear quadratic model and in addition cells were subjected to the bystander effect.Some simulations were run in the case of two cell lines, the hamster cell line V79 and the glioma cell line T98G. The results show that the bystander effect is unlikely to be limited to one period of the cell cycle, but that the low dose hyper-radiosensitivity and the bystander effect could be the same phenomenon. This work also suggests that the bystander effect may be significant after low doses of conventional radiotherapy. Such a model represents a very useful tool for solving problems that at the moment cannot be investigated experimentally.