The machine automatically lays rolls of magnetic tapes onto overlay material. Using heat and pressure, the magnetic tape is bonded to the overlay material, while the backing foil is rewound to a single rewind stand after the laying process. The machine can be built to operate for roll to roll or roll to sheet application. When operating roll to roll, the overlay is rewound after the tape is laid. When operating roll to sheet, after the tape is laid, the material is cut to the desired length with a guillotine. The material thickness of roll overlay material can range from 1-10 mil. The machine can be built to operate roll to roll or roll to sheet or roll to roll and roll to sheet applications.