A magnet system comprises magnetic field generating means such as a superconducting magnet (12) and a shield including a number of sheets (9) of magnetic material, the size (1 z , 1 x ) and position (r) of the or each sheet (9) relatively to the magnetic field generating means (12) being such that in use at the edge of the sheet or sheets the component of magnetisation (M z ) parallel to the sheet in the direction of the magnetic field is less than or substantially equal to zero.