The finite element method (FEM) is widely used for modeling wave propagation and stiffness reconstruction in magnetic resonance elastography (MRE). However, it is not that efficient for modeling inclusions with complex interfaces. Here, we propose a formulation of FEM known as the eXtended FEM (XFEM), and investigate this method in two studies: wave propagation across an oblique linear interface and stiffness reconstruction of a random-shape inclusion. XFEM results present good agreement with the theoretical predictions and FEM simulation results. XFEM can be regarded as an ideal alternative to FEM for inclusion modeling in MRE.