Limited diffraction beams such as Bessel beams and X waves have large depth of field and could have applications in medical ultrasound and other wave related areas. However, they are usually produced by annular arrays which have to be scanned mechanically. In this paper, the production and steering of the limited diffraction beams with a two-dimensional array are studied. Results show that good limited diffraction beams can be produced if the size of the array elements is small and the array aperture is compensated so that the projection of the aperture on a plane perpendicular to the beam axis is a constant annular ring pattern. The electronic system for controlling the two-dimensional array is described and methods to simplify it are proposed.