This paper reports the first predictions of the yield stress of suspensions of non-Brownian magnetic fibers in the presence of uniform magnetic fields. The quasistatic regime of the shear deformation (before the flow onset) of the suspension is studied. Four different structures of the magnetic fiber suspensions are considered-column, zigzag, three-dimensional stochastic and near-planar stochastic structures-and the yield stress is attributed to the failure of the given structure at a critical strain. The main contributions to the yield stress are found to come from the restoring magnetic torque acting on each fiber and from the solid friction between fibers. The enhanced magnetorheological effect of magnetic fiber suspensions observed experimentally [M. T. Lopez-Lopez , J. Rheol. 53, 115-126 (2009)] is explained and quantified in terms of interfiber friction. Surprisingly, the dipolar magnetic interactions between fibers do not affect significantly the yield stress. The lowest yield stress is obtained for the zigzag structure and the highest one for the column structure. A reasonable agreement with the experiments is obtained for 5% and 7% fiber volume fractions in the frame of the more realistic model of near-planar stochastic structures.