This work deals with the magnetic field-induced static yield stress of magnetorheological (MR) suspensions with concentration near the limit of maximum-packing fraction. With this aim, homogeneous suspensions of iron microparticles with 50 vol.% concentration were prepared, and their yield stress measured as a function of the applied magnetic field. In view of the failure of existing models to predict, on the basis of realistic hypotheses, the values of the yield stress of highly concentrated MR suspensions, we developed a new model. Our model considers that field application induces body-centered tetragonal structures. Upon shearing, these structures deform in such a way that interparticle gaps appear between neighboring particles of the same chain, whereas the approach of particles of parallel chains ensures the mechanical stability of the whole multi-chain structure. Based on this hypothesis, and using finite element method simulations of interparticle magnetic interactions, our model is able to quantitatively predict the yield stress of highly concentrated MR suspensions. Furthermore, estimations show that the main contribution to the field-dependent part of the yield stress comes from the change in the permeability of the structures as interparticle gaps are enlarged by the shear. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.4731659]