This invention relates to an apparatus for continuously supplying a web of sheet material wound on a roll to a machine, such as a printing press, which draws the web off the roll. In such an apparatus, the web is drawn from an active roll at an active station and, when the running web is nearly exhausted, it is spliced to the web of a standby roll located at a splicing station. Preparatory to splicing, the standby roll is turned and accelerated until its periphery speed is equal to the linear speed of the running web and then the running web is pasted to the web on the standby roll and severed from the active roll. Thereafter, the standby roll is moved to the active station while the web is being drawn from it and this roll becomes the new active roll. While the running web is being drawn from the active roll, a core brake responsive to the tension of the running web applies a drag to the core on which the web is wound to control the web tension. The active and the standby rolls turn about horizontally spaced parallel axes and a conveyor advances the new active roll from the standby station to the active station. An example of such an apparatus is disclosed in Curran et al U.S. Pat. No. 4,173,314.