A method of the type in which a strip of rubber is moved continuously from a rubber-supplier device to a consumer device. During the continuous movement and prior to reaching the consumer device, a portion, referred to as the residue, is taken continuously from the strip of rubber. The residue is taken by continuously cutting the strip of rubber. For example, the supplier device includes upstream storage means for storing the strip of rubber from which the strip is moved toward the extruder, and downstream storage means in which the residue is stored. After the strip of rubber on the upstream storage means has been used up, the upstream and downstream storage means are swapped with each other.