In a tire for vehicle wheels, each of the two annular anchoring structures includes at least two annular reinforcing inserts, each of them being made up of at least one first elongated element and at least two reinforcing elements that are mutually spaced apart and each of which extends in a radial direction and includes at least one second elongated element. An end portion of at least one carcass ply lies between two adjacent annular reinforcing inserts. The second elongated element of at least one of the reinforcing elements is of metal material and delimits an angle included between about 20° and about 70° relative to a radial direction passing through a radially internal point thereof.