The nuclear magnetic resonance machine comprises a device (101) for creating an intense main magnetic field B.sub.0 in a useable interior space (109) in the form of a tunnel with axis Z, a device for radio-frequency excitation and processing of radio-frequency signals emitted in response by a body (150) placed in the useable interior space (109), and a set (110) of solenoidal gradient coils for superimposing on the intense magnetic field B.sub.0 components of an additional magnetic field, the gradient coils (111-122) being incorporated into tubes that are disposed in a annular cylindrical space (130). Between an exterior cryogenic enclosure (102) and the annular cylindrical space (130) a cylindrical screen (104) is disposed along the axis Z comprising a conductive material of low resistance and low magnetoresistance such that negligible induced currents are generated in the exterior cryogenic enclosure (102) while the eddy currents induced in the cylindrical screen (104) contribute to reinforcing the gradients produced by the solenoidal gradient coils (111-122).