Noninvasive image-based measurement of intrinsic tissue pressure is of great interest in the diagnosis and characterization of diseases. Therefore, we propose to exploit the capability of phase-contrast MRI to measure three-dimensional vector fields of tissue motion for deriving volumetric strain induced by external vibration. Volumetric strain as given by the divergence of mechanical displacement fields is related to tissue compressibility and is thus sensitive to the state of tissue pressure. This principle is demonstrated by the measurement of three-dimensional vector fields of 50-Hz oscillations in a compressible agarose phantom and in the lungs of nine healthy volunteers. In the phantom, the magnitude of the oscillating divergence increased by about 400% with 4.8 bar excess air pressure, corresponding to an effective-medium compression modulus of 230 MPa. In lungs, the averaged divergence magnitude increased in all volunteers (N = 9) between 7 and 78% from expiration to inspiration. Measuring volumetric strain by MRI provides a compression-sensitive parameter of tissue mechanics, which varies with the respiratory state in the lungs. In future clinical applications for diagnosis and characterization of lung emphysema, fibrosis, or cancer, divergence-sensitive MRI may serve as a noninvasive marker sensitive to disease-related alterations of regional elastic recoil pressure in the lungs. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.