This paper is concerned with the development of a material model for the constituents of a magnetoactive compo-site. Special attention is paid to magnetorheological elastomers which are synthesized from a soft polymeric matrixmaterial with embedded magnetizable particles. Because the particles interact under an applied magnetic load,a coupled magneto-mechanical field problem has to be solved. The mechanical properties of the polymer matrixmotivate the consideration of large deformations. We present the balance equations with boundary conditions andan appropriate material model. The corresponding boundary value problems are solved by the Finite-Element-Method. A weak numerical coupling scheme enables the staggered solution of two subproblems, the stationarymagnetic and mechanical one. The coupling between both is realized by a surrounding iterative loop.