A device for continuously sheathing a ply of threads, said ply being formed by an array of approximately mutually parallel threads. The device includes a thread guide, a coating chamber into which a first feed channel and a second feed channel run, which are independent of each other, connected to a first feed device and to a second feed device respectively and capable of delivering a first material and a second material under pressure and with a defined flow rate, and the outlets of which channels are placed above and below the plane of the ply of threads, and an output die. Pressure-measuring device, connected to a controller for controlling the pressure of each of the feed devices, are placed in the coating chamber facing and in line with each other, on either side of the plane of the ply and in the immediate vicinity of the outlet for the feed channels.