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Recently, a new class of biocompatible elastic polymers loaded with small ferrous particles (magnetoelastomer) was developed at Lawrence Livermore National Laboratory, Livermore, CA. This new material was formed as a thin film using spin casting. The deformation of this material using a magnetic field has many possible applications to microfluidics. Two methods will be used to calculate the deformation of a circular magnetoelastomeric film subjected to a magnetic field. The first method is an arbitrary Lagrangian-Eulerian (ALE) finite-element method (FEM) and the second is based on nonlinear continuum electromagnetism and continuum elasticity in the membrane limit. The comparison of these two methods is used to test/validate the FEM.