A theory is presented for the distribution in size of deletions induced by ionizing radiation, based on three assumptions: (1) deletions that are observed delete part or all of a gene to make a mutation, but not adjacent DNA sequences essential for survival of the mutant; (2) deletions are distributed at random along the DNA; (3) the probability of formation is proportional to the rate at which the two endpoints, which must meet to form the deletion, collide with each other. Experimental data for radiation-induced deletions in human and hamster hprt genes are in good agreement with calculations that assume the inducing lesion does not break the intracellular chromatin fiber; calculations assuming the inducing lesion is a break are not a good fit to the data. The low frequency of deletions observed in the hamster aprt gene is shown to be a consequence of the small gene size and the presence of a nearby essential DNA sequence, ensuring that most deletions affecting the gene also delete the essential sequence and are thus not observed.