Abstract: The process is of the type comprising continuously shaping a mixture of thermoplastic material and crosslinking agent by pressure and then effecting the cross-linking by the cross-linking agent. The cross-linkable mixture is placed inside a sintering zone in which it is subjected to the action of pressure and a sintering temperature at the same time as it is put into shape. It is then conveyed without modification of shape by means of the same pressure to a zone where the cross-linking is effected by a rise in temperature. The device comprises in the following order, along a common axis, a device supplying the cross-linkable mixture, a sintering die and a cross-linking die. These dies define a continuous space in which the pressure is exerted and each comprise heating means.