Abstract: The invention relates to a method for flame cutting a part made of a metal containing iron, implementing at least one blowtorch having a cutting nozzle, wherein the operation is carried out according to the steps of preheating a localized area of the part by means of a flame obtained by the combustion of a combustible gas and oxygen, then directing the gaseous oxygen towards the preheated localized area into a first pressure and/or first flow for initiating a bore while shifting the blowtorch in the cutting direction. Then, after initiating a bore in the part, the pressure and/or flow of gaseous oxygen is increased in the direction of the bore start area to a second pressure higher than the first pressure and/or a second flow higher than the first flow to obtain the complete bore in the part. The invention also relates to associated equipment.