An improved ultrasonic pulse-echo method and apparatus that has particular application in making precision measurements of compressibility in any backscattering material, in particular organic tissue, is disclosed. The method employs a standard transducer or transducer containing device which is translated transaxially, thereby compressing or displacing a proximal region of a target body in small known increments. At each increment, a pulse is emitted and an echo sequence (A-line) is detected from regions within the target along the sonic travel path or beam of the transducer. Resulting time shifts in echo segments corresponding to features in the target, corrected for regions of varying sonic speed along the sonic path, provide relative and quantitative information concerning the strain caused by the compressions. The stress imparted by the transducer and containing device is also determined, corrected for depth along the sonic path. The appropriate values for stress are divided into the respective values for strain along each path to yield an elastogram, or array of compressibility values, of the target.