The yield stress of a magnetorheological suspension is calculated from two different approaches. The first one is based on a mesoscopic description of the structure taking only into account the shape anisotropy of the strained aggregates. The second one is based on a microscopic approach where the interparticle forces, due to the application of the field, are calculated numerically by taking into account the magnetostatics between the particles inside the aggregates. We show that the macroscopic description well applies to suspensions of nonmagnetic particles in a ferrofluid and that a layered structure, consisting of parallel slabs of magnetizable materials should have a yield stress much higher than a structure made of cylindrical aggregates. On the other hand the microscopic approach is appropriated for the description of suspensions of particles of high permeability. In this case, the yield stress is mainly determined by the rupture between pairs of particles and, consequently, it strongly increases with the angle between the line of centers of the pair undergoing the rupture and the field.