Abstract: A process is provided for the construction of a composite tube comprising a metal tube, in particular a tube of copper, and a cladding of tubular form into which the said tube is inserted, the material of the said cladding being constituted by a deformable foam material, in particular foam rubber, characterized by the fact that it comprises at least a first phase in which a section of said cladding of predetermined length is disposed in a configuration with its axis substantially rectilinear, a second phase in which a fluid under pressure is fed from a first end of the said cladding to the interior thereof, while at the other end there is introduced one end of the said tube in such a way as to cause, by the action of the said fluid under pressure, a radial deformation of the said cladding, and a third phase in which the said copper tube is introduced axially into the interior of the said cladding while it is deformed radially.