Variable length storage of running length material between stations in a web handling or processing line in which storage of the self-supporting portion of the variable length is nearly constant in length independent of the total length of the stored loop. The sides of the stored variable length loop are held against the respective surfaces of a pair of opposed and nearly vertical endless belts each of which belt is drivable in a direction generally opposite to that of the other belt. Each belt is driven independently of the other belt by drive means at least one of which is controlled in response to a pair of sensors respectively detecting the predetermined maximum and minimum extents of the length of the stored loop. In the particular and proximate utility of the invention, the web being handled comprises bias-cut wire fabric breaker belt stock for use in pneumatic tires. The respective sides of the variable length loop are held against the associated surfaces of the belts to insure movement of the web together therewith by a plurality of magnets arranged to act through the belt.