The cosmic ray minicycle of 1974 is a medium-term modulation event where a clear anticorrelation is observed between the cosmic ray intensity and the heliospheric magnetic field magnitude B. It occurs during a period of minimum solar activity in an A>0 magnetic polarity epoch. Cosmic ray modulation during the event is studied with an analytical, spherically symmetric approximation for a propagating diffusive barrier. Under the assumption that the cosmic ray radial diffusion coefficient K scales inversely with B, the temporal development of the disturbance can be obtained from the observed variation of B. A recovery process is described by a simple exponential, with a constant recovery time throughout the event. The profile of the intensity decrease as predicted by the model varies with the temporal development of the disturbance and with the duration of the disturbance in relation to the recovery timescale. The model predicts a maximum depression which is about a factor of 2.5 too small compared with neutron monitor observations. A replacement of the inverse relation K∝1/B by the more general case K∝B-n and a value of n~2.5 leads to a good agreement between model and observations. It is remarkable how closely the high-energy cosmic ray intensity follows the temporal structure of the magnetic field magnitude, suggesting that the magnetic field enhancement plays an important role for modulation during the minicycle. For the period under study, radial diffusion is essentially determined by diffusion parallel to the average field. Based on quasilinear theory a variation K∥∝B-2 is suggested, consistent with the value of n=2.5¿1.0 derived in the paper. ¿ 2000 American Geophysical Union