The following paper presents an idea of minimising the number of connections of individual piezoelectric transducers in a row-column multielement passive matrix system used for imaging of biological media structure by means of ultrasonic projection. It allows to achieve significant directivity with acceptable input impedance decrease. This concept was verified by designing a model of a passive ultrasonic matrix consisting of 16 elementary piezoceramic transducers, with electrode attachments optimised by means of electronic switches in rows and columns. Distributions of acoustic field generated by the constructed matrix model in water and results of the calculations conformed well.