Magnetorheological elastomers consist of natural or synthetic rubber filled with micron-sized magnetizable particles. During curing of the elastomer, an applied magnetic field aligns the particles into chains. The shear modulus of the resulting cured material is sensitive to magnetic fields of several kOe magnitude. Such sensitivity to magnetic field makes these materials attractive for applications in automotive mounting components. At large fields (magnetic induction B>1 T), the Fe particles are completely magnetized or saturated. Calculations using finite element analysis show that for typical elastomers the increase in shear modulus due to interparticle magnetic forces at saturation is about 50% of the zero-field modulus. The optimum particle volume fraction for the largest fractional change in modulus at saturation is predicted to be 27%. Calculations of the zero-field shear modulus perpendicular to the chain axis indicate that it does not exceed the modulus of a filled elastomer with randomly dispersed particles of the same concentration.