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. A mold for the grid is filled with an acoustically absorbent material such that the absorbent material fills the spaces between the contacts, so as to produce a block when cured. The common base is removed so as to separate the contacts from one another within the block. Further machining exposes the opposite ends of micro-contacts so that a like number of contact faces or pads are provided at opposed surfaces of the backing layer. Improved transducer constructions are also disclosed.