In a process for the manufacture of a blade/vane of a turbomachine, the blade/vane is made of a metallic enveloping structure and a supporting structure made of composite material provided inside of the enveloping structure and suitably joined to the enveloping structure. A metal-felt weave is welded or soldered/brazed to the sheet making up the enveloping structure, whereupon this sheet-weave-assembly is shaped by hydroforming or an internal high-pressure forming process to provide the enveloping structure of the blade/vane. Finally, the composite material making up the supporting structure is introduced into the cavity of the enveloping structure.