A method is provided for making a backing layer for an ultrasonic matrix array transducer useful in medical imaging and the like. A conductive grid is provided which includes a plurality of micro-contacts each joined together by a common base so that spaces are provided between the free ends of the contacts. The method includes placing the grid in a mold, filling the mold with an acoustically absorbent material such that the absorbent material fills the spaces between the contacts, curing the material in the mold so as to form a block formed by the cured absorbent material and the grid, and releasing the block from the mold. The common base is removed by, e.g., machining the grid, so as to separate the contacts from one another within the block. Further machining is used to expose the opposite ends of micro-contacts so that a like number of contact faces are provided at opposed surfaces of the backing layer so formed. The grid can be prepared in several ways. Improved transducer constructions are also disclosed.