A supply roll (20) of thin liner material (22) for carrying a strip (24, 26) of resilient plastic material is mounted for rotation with the axis of rotation (B-B) in a horizontal position. An arm (28) is mounted adjacent the supply roll (20) for swinging movement toward and away from the axis of rotation (B-B) of the roll. A peel-off roller (32) is mounted on the distal end of the arm (28) and is rotatable for rolling engagement with the supply roll (20). The liner material carrying the strip (24, 26) of resilient plastic material is directed around the peel-off roller (32) and over an idler roller (34) located at a position such that a force component acting on the arm (28) resulting from the tension in the liner (22) is in the direction of the supply roll (20) for urging the peel-off roller (32) against the supply roll (20). This provides a regular and minimal tension in the liner (22) while the liner (22) is pulled off the supply roll (20) over the idler roller (34) and to a driven liner take-up (38). The diameter of the peel-off roller (32) is small as compared to the diameter of the supply roll (20) causing the liner (22) to undergo a sharp change in direction when leaving the supply roll (20) which facilitates the peeling off of the liner (22). After passing around the idler roller (34) the liner (22) carrying the strip (24, 26) of resilient plastic material passes over a separating roller (36) for separating the strip (24, 26) of resilient plastic material from the liner (22) so that it can be directed to a tire building machine or other apparatus for utilizing the strip (24, 26) of resilient plastic material.