A method for magnetic resonance elastography (“MRE”) is described, in which an MRE inversion that accounts for waves propagating in a finite, bounded media is employed. A vibratory motion is induced in a subject and MRE is performed to measure one or more components of the resulting displacement produced in the subject. This displacement data is subsequently filtered to provide a more accurate and computationally efficient method of inversion. Wave equations based on the geometry of the bounded media are then utilized to calculate the material properties of the subject. Such a method allows for the performance of MRE on tissues such as the heart, eye, bladder, and prostate with more accurate results.