The relative success of manual palpation in the detection of breast cancer would suggest that a method for remote palpation resulting in a measurement of tissue elasticity could provide a diagnostic tool for detecting cancerous lesions deeper within the breast. This presumption is based in part on the excellent contrast between neoplastic and normal tissue due to the large (orders of magnitude) relative variation in the shear elastic modulus. By comparison, the bulk deformational modulus maintains the same value to within 20% for most soft tissues. A specific method of magnetic‐resonance imaging (MRI) which measures tissue displacements has been used in experiments with a phantom containing regions of increased Young's modulus as a demonstration. The spatial modulation of magnetization technique uses the displacement of a spatial grid pattern caused by spin saturation to track regional motion. Mathematical reconstruction of the distribution of elastic moduli is shown for select examples. Any modality, e.g., MRI, ultrasound, etc., which can detect local tissue motion with sufficient spatial resolution can be used and therefore the results presented here should give an indication of the utility of such motion tracking techniques to future measurement of tissue elasticity.