A biologically based model is developed for normal tissue complication probability as a function of dose and irradiated volume fraction for organs such as the kidney and the lung. The organ is assumed to be composed of functional subunits (FSUs) which are arranged in a parallel architecture. The complication is produced only if a sufficiently large fraction of the FSUs are inactivated by radiation and an FSU is inactivated only when all the clonogenic cells within it are killed. The linear-quadratic model is used for the dose-response of individual cells within an FSU. The predictions of this model are compared with those of an empirical power law function for uniform whole and partial organ irradiation.