The present disclosure provides a method for manufacturing a preform made of reinforcement fibers woven in a longitudinal direction. The preform is impregnated with resin in order to form an elongated element having a variable transverse cross-section. In one form, the method includes the step of simultaneously including a reduction (or increase) in width and an increase (or reduction) in height. The variable cross-section includes, along the length thereof, a consistent number (c) of continuous warp threads arranged in layers. The method for reducing width includes carrying out a change in weave, adding additional weft threads, and simultaneously drawing the teeth of the longitudinal beater reed closer together so as to increase the number of layers.