An impulsive differential equation model of cancer treatment by radiation therapy (RT) is studied. Analytical results for the model's persistence and eradication of cancer cell volumes are obtained to illuminate the dynamics between tumor growth and RT. It is also shown that, although periodic solutions may exist, they are necessarily unstable. A modified model is then proposed, assuming that RT is more effective than the first model assumes. In addition to similar results as for the original model, conditions are obtained under which periodic solution exists and is globally stable, showing the possibility that regression can occur in periodicity. Numerical simulations are provided to confirm the results.