A method for calculating a mechanical property of a material using a magnetic resonance imaging (“MRI”) system is provided. The method is particularly robust to image data having low signal-to-noise ratio (“SNR”). An MRI system is used to acquire magnetic resonance elastography (“MRE”) data from a subject containing the material. Exemplary materials include lung tissue. Images are reconstructed from the MRE data and used to produce a wave image from which a spatial frequency spectrum is produced. A principal frequency of the spatial frequency spectrum is produced and used to calculate a mechanical property of the material. For example, shear stiffness may be calculated.