For an arcuate structural member (10) of a fuselage frame, tapes of resin pre-impregnated unidirectional fibers are used. The member (10) includes a web (11) lying in a radial plane and a radially outer cylindrical flange (12). An elongate, arcuate forming mandrel (M1) having a flat radial surface (F) forming an angular edge (D) with a radially outer, convex cylindrical surface (S) is used and a series of promontories (P) radiating outwardly with respect to the cylindrical surface (S) are provided. Layers of pre-impregnated composite material are laid on the mandrel (M1) to form a first flat arcuate laminate (20′), with a part (20″) of the laminate projecting radially outwardly beyond the angular edge (D). The mandrel (M1), the laminate (20′) and the promontories (P) are covered with a membrane (E). A vacuum is then applied to urge the projecting part (20″) of the laminate against the cylindrical surface (S) and against the promontories (P). Contact of the projecting part (20″) with the cylindrical surface (S) near the promontories is prevented or retarded. Finally, discrete portions of the projecting part (20″) near the promontories are removed, obtaining peripheral cavities (15) spaced apart from one another.