A process for forming a cover for an industrial roll includes the steps of: providing an elongate cylindrical core having a longitudinal axis; rotating the core about the longitudinal axis; providing a nozzle movable along a nozzle path that is substantially parallel to and above the core longitudinal axis, the nozzle having at least an upstream outlet and a downstream outlet, the nozzle outlets being longitudinally offset a distance from each other; and applying multiple strips of polymeric material to the core through the nozzle outlets as the nozzle moves along the nozzle path such that the downstream strip forms an overlapping spiral inner layer and the upstream strip forms an overlapping spiral outer layer that overlies the inner layer, the inner and outer layers being adhered with the core.