General expressions for the yield stress of a magnetorheological substance are derived in this work from consideration of unsymmetric elastic and magnetic stress states of a continuum. Geometrical models of composites illustrate use of the general expressions to obtain closed‐form analytical formulas exhibiting the dependence of the shear stress on shear strain, magnetic susceptibility and volumetric loading of the composite materials, demagnetization coefficient, and the applied field intensity over the full range of composition and shear strain. The model prediction recovers scaling behavior known from laboratory experiments, and values of shear modulus that compare in order of magnitude and trend with existing values determined from dipole–dipole and finite element analyses. Duality of electro‐ and magnetopolarized systems permits the results to be applied to the polarization component of the electrorheological response.