A method for cutting a strand of a continuous casting, wherein the cross-section of said casting has a plurality of sections having different thicknesses, said cross-section being preferably circular or elliptical or H-shaped, comprising the following steps: - providing at least one cutting and heating device in correspondence with said strand to be cut, - handling said cutting and heating device in a plurality of different cutting and heating working positions (P0-P20) of said strand to be cut, - feeding to the cutting and heating device: a first fluid for heating the strand of continuous casting to be cut and a second fluid for cutting said casting strand; wherein the flowrate of said first heating fluid and/or of said second cutting fluid fed to said cutting and heating device changes while said strand is being heated and/or cut; characterized in that: - the cross-section of the strand of the continuous casting to be cut is divided into a plurality of subsections (Z1-Z20) having different thicknesses (S1-S19), - each of said subsections (Z1-Z20) is associated to a predetermined flowrate of the second cutting fluid and/or of the first heating fluid to be fed to said cutting and heating device, and in that it includes the following steps: - detecting the position of the cutting and heating device during cutting and/or heating with respect to said subsections (Z1-Z20) into which the cross-section of the casting strand to be cut has been divided, - depending on the detected position of the cutting and heating device, the flowrate of the second cutting fluid and/or of the first heating fluid fed to the cutting and heating device is adjusted according to the flowrate values associated to the subsection (Z1-Z20) of the cross-section where the cutting and heating device is situated. - providing at least one cutting and heating device in correspondence with said strand to be cut, - handling said cutting and heating device in a plurality of different cutting and heating working positions (P0-P20) of said strand to be cut, - feeding to the cutting and heating device: a first fluid for heating the strand of continuous casting to be cut and a second fluid for cutting said casting strand; - the cross-section of the strand of the continuous casting to be cut is divided into a plurality of subsections (Z1-Z20) having different thicknesses (S1-S19), - each of said subsections (Z1-Z20) is associated to a predetermined flowrate of the second cutting fluid and/or of the first heating fluid to be fed to said cutting and heating device, and in that it includes the following steps: - detecting the position of the cutting and heating device during cutting and/or heating with respect to said subsections (Z1-Z20) into which the cross-section of the casting strand to be cut has been divided, - depending on the detected position of the cutting and heating device, the flowrate of the second cutting fluid and/or of the first heating fluid fed to the cutting and heating device is adjusted according to the flowrate values associated to the subsection (Z1-Z20) of the cross-section where the cutting and heating device is situated. - detecting the position of the cutting and heating device during cutting and/or heating with respect to said subsections (Z1-Z20) into which the cross-section of the casting strand to be cut has been divided, - depending on the detected position of the cutting and heating device, the flowrate of the second cutting fluid and/or of the first heating fluid fed to the cutting and heating device is adjusted according to the flowrate values associated to the subsection (Z1-Z20) of the cross-section where the cutting and heating device is situated.