The process can include moving the web across a laser-cutting window in a longitudinal direction while maintaining a main tension in the web, the main tension being in the longitudinal direction applying a specific tension to at least a portion of the web and cutting a portion of the shape by moving the laser beam along the portion of the shape, within the laser-cutting window, during said moving of the web, and while maintaining at least a portion of the specific tension at the laser beam in an orientation different than the instantaneous orientation of movement of the laser beam.
