The vector nature of the NMR signal gives rise to a group of displacement imaging methods in magnetic resonance imaging that are based on spin phase-shifts. They are suited for studying physiological motions such as the heartbeat and elastic reponses of arterial walls to the blood pressure. Elevated myocardial stiffness is a cause of high diastolic blood pressure and congestive heart failure. The traditional measure of heart chamber stiffness uses diagnostic catheterization, an invasive procedure not acceptable for many patients. MR elastic displacement imaging is a new way to estimate material viscoelastic parameters non-invasively. It has been validated in animal models and shown feasible in humans. Clinical trials to detect heart and artery stiffening in patients with congenital heart disease are being prepared.