Abstract: Methods and apparatus for inducing necrosis and degradation of blood vessels are described. The invention is suitable to treat various conditions such as varicose veins and telangiectasia. The apparatus for inducing degradation of a blood vessel in a tissue, e.g., skin, includes an external energy source that non-invasively delivers to the blood vessel energy that is preferentially absorbed by the blood vessel to heat the blood vessel walls to a temperature of at least about 60 degrees centigrade, and a pressure source connected to the energy source to collapse the blood vessel once the blood vessel walls have been heated to at least about 60 degrees centigrade for a period of time and with a force sufficient to permanently weld the apposed walls of the blood vessel together, whereby the blood vessel undergoes necrosis and degradation.