Disclosed is a method and apparatus for generating high pressure steam within a well bore. The steam vapor generator is constructed for receiving and mixing high pressure water, fuel and oxidant in a down-hole configuration. High pressure water is received within a heat exchanger constructed around a combustion chamber in an annular sleeve configuration and heated through a thermal wall region forming a lower portion thereof. The combustion chamber utilizes the heat energy of radiation to heat the water flowing in the annular sleeve to the point of steam. The heat exchanger further includes a series of open ended flow tubes which triplicate the length of the flow path of the water prior to egressing from the sleeve. A collection chamber is provided beneath the combustion chamber in communication with the heat exchanger for the mixing of the high pressure vapor and the exhaust thereof into the adjacent well formation.