Iterative algorithms can provide a feasible solution, if any exists, to specified treatment goals. Our model subdivides both the patient's cross section into a fine grid of points and the radiation beam into a set of "pencil" rays. The anatomy, treatment machine parameters, dose limits and homogeneity, are all defined. This process of subdivision leads to a large system of linear inequalities with a solution that provides a radiation intensity distribution that will deliver a prescribed dose distribution. The clinical results from two different algorithms will be presented and contrasted. Once the anatomy, treatment, and machine parameters have been entered, the computerized algorithms yield an answer in several minutes. The Cimmino algorithm also allows "weights" or priority assignments of the treatment goals. The resulting solution is biased towards fulfilling the specified doses for the anatomic regions which were given greater weight. It is desirable to have a systematic search of possible treatment alternatives in complex clinical situations, including 3-dimensional radiation therapy treatment planning (RTTP). Our method has been applied to 2-D RTTP, but is equally applicable to 3-D RTTP with minor modifications.