Trapping and manipulating micrometer-scale particles in fluids is of interest in the biosciences. The work reported here uses a method whereby ultrasonic standing waves are generated using counter-propagating ultrasonic waves in order to generate standing waves with nodal positions that can be determined by adjusting the relative phases of the waves. The acoustic radiation force acts to drive dense particles to nodes of the standing wave. Varying the relative phase of the signals applied to each transducer allows the positions of the nodes, and hence the particles to be varied. Two pairs of opposing transducers, positioned orthogonally and with appropriate relative phases (determined analytically) applied are used. This allows trapping of particles on a grid and manipulation in two dimensions. The technique was demonstrated using 10-micron-diameter polystyrene spheres in water. The spheres were levitated on planes using a levitation transducer and then 5 MHz signals applied to the four matched transducers. It was shown that by varying the relative phases applied to the transducers the particles could be forced onto a grid pattern, with a half-wavelength (0.15 mm) separation, and then the grid translated across the plane in arbitrary directions. It was shown that the relationship between phase and position agreed with that expected analytically. This approach represents an opportunity to develop a new class of dexterous particle manipulation devices and it is anticipated that this approach will be applied in the biosciences.