The operation of a micro-pump system driven by a magnetoelastic polymeric membrane developed at Texas A&M University is analyzed by numerical simulations. Unsteady, incompressible Navier-Stokes equations in a moving boundary system are solved by a spectral element methodology, employing an Arbitrary Lagrangian Eulerian (ALE) formulation on unstructured meshes. The performance of the micro-pump is evaluated as a function of the Reynolds number and the geometric parameters. The volumetric flowrate is shown to increase as a function of the Reynolds number. The system is simulated by assuming the deformation of the membrane. The required voltage and current are then calculated by a lumped parameter analysis.