A method and catheter for use in practicing the method are provided by which a highly concentrated medication or chemotherapeutic agent can be applied locally under sufficient pressure to cause the medication or agent to penetrate into the localized tissue. The total volume of medication or agent is quite small, well below levels that might cause an adverse reaction in other parts of the body. The catheter includes a thin walled flexible balloon having a plurality of minute holes through which medication may flow at a low flow rate. The balloon is inflated with the medication under pressure and the flow rate of the order of a few ccs per minute is controlled by the minute holes in the balloon. In practicing the method of the invention, the balloon is selected such that its inflated diameter will correspond to or be slightly greater than the diameter of the lumen into which it is to be placed so that when the balloon is inflated, it will contact intimately the surface of the lumen. Inflation of the balloon with the medication will cause a thin film to spread between the balloon and the lumen, the film being maintained under a sufficient pressure to penetrate significantly the surrounding tissue with a high concentration of medication. The quantity of medication that ultimately flows free into the lumen is quite small and is insufficient to cause any other damage to the patient.