A two-dimensional array allows rapid three-dimensional ultrasound scanning. A high volume-per-second scan rate using a limited number of system channels (e.g. 192, 256 or other number of channels) is provided by a transducer array without beamforming circuitry in the probe. A fan beam of acoustic energy is transmitted along a scan plane from transducer elements that extend lengthwise over a substantial portion of the lateral aperture. Rows of these long transmit elements are provided along the elevation aperture for electronic steering of the fan beam in the elevation dimension. One or more rows of smaller receive elements are used for forming beams each representing a scan line along the lateral dimension in response to each transmission of a fan beam. Elevation resolution is provided primarily from the elevationally spaced transmit elements and partially from two or more rows of laterally spaced receive elements. The lateral resolution is responsive to the lateral spacing of the receive elements.