invention relates to a method of dimensioning a riser assembly intended for offshore drilling connecting an underwater wellhead to a floating support comprising a main pipe wherein the following stages are carried out selecting a complete architecture for the riser assembly from specifications notably by fixing the thickness of the main pipe and of the buoyancy means and calculating the apparent weight of this assembly determining the tension margin at the top of the assembly when disconnected from the wellhead considering the apparent weight and the tension amplified at the top by the motion of the floating support from which the assembly is suspended in cases where the tension margin corresponds to a value close to a determined value calculating the von mises stresses in all the sections of the pipe when connected to the wellhead in cases where the stresses are close to a criterion determined in connection with the yield limit of the material of the pipe checking by calculation the load on each component of the riser assembly and its fatigue under dynamic conditions application_number US 15376802 A description in fig1 reference number 1 refers to the entire riser the underwater wellhead is diagrammatically shown by reference number 2 the riser is connected to wellhead 2 by.