A method for manufacturing a composite material part comprising a web and at least one flange. In a laying up stage, a plurality of plies of different orientations, including 0° oriented plies, are laid up to obtain a flat laminate with edges comprising an outer contour and an inner contour, the flat laminate also comprising at least one section with a radius of curvature of less than 10 m. A forming stage comprises forming a fold along a folding line on the flat laminate to create a flange forming an angle with the web, and applying a stress tension to the 0° oriented plies located at least partially between the folding line and the outer contour of the flat laminate, in the at least one section, to avoid the appearance of wrinkles.