A conformal oven which has flexible sidewalls for enabling it to conform to and seal against a contoured surface. A vacuum sealing bag is sealed over a patch on a contoured surface such as an airplane wing made of an epoxy composite material. A vacuum is created within a vacuum sealing bag over the patch and the oven is placed over the patch and is sealed against the contoured surface being patched. A partial vacuum is created within the oven to maintain the seal against the contoured surface. The atmosphere within the oven is heated by force convection of air, electric heating or other alternative heating means to cure the patch within the evacuated vacuum sealing bag.The conformal oven is formed with flexible sidewalls, preferably accordian-like in shape, to enable the open end of the oven to conform to the contoured surface being patched and to enable sealing of the open end of the oven to the contoured surface in order to perform the curing process.