A theoretical model of magnetoviscous effect in a suspension of nonBrownian linearly magnetizable particles is suggested. A simple shear flow in the presence of an external magnetic field aligned with the velocity gradient is considered. Under the action of the applied field, the particles are supposed to form dense highly elongated droplike aggregates. Two different scenarios of the aggregates' destruction under shearing forces are considered, namely, a “bulk” destruction of aggregates into pieces and an “erosive” destruction connected to the rupture of individual particles from the aggregate surface. Both models are based on a balance of forces acting either on the whole aggregate or on individual particles. The two approaches lead to qualitatively different Mason number (Ma) behaviors of the magnetic suspensions: The suspension viscosity scales as either Ma−2/3 for the bulk destruction of aggregates or Ma−4/5 for the erosive destruction. In any case, we do not recover Bingham behavior (Ma−1) often predicted by chain models of the magneto- or electrorheology. Our theoretical results are discussed in view of comparison with existing theories and experimental results in the wide range of Mason numbers.