Two-dimensional (2-D) arrays are useful for improving quality of three-dimensional (3-D) medical imaging in ultrasound. Beams produced with a 2-D array are usually simulated with the Rayleigh–Sommerfeld diffraction formula (RSDF). In general, the RSDF requires a 2-D integration for each field point in space and thus is very time consuming. Fresnel approximation may reduce the 2-D integration to 1-D but will not yield satisfactory results near the transducer surface or for field at a large angle from the beam axis. In this work, limited diffraction array beams are used to synthesize beams produced with a 2-D array [J.-Y. Lu, Int. J. Imaging Syst. Technol. 8, 126–136 (1997)]. In this method, the 2-D integration is replaced with a 2-D summation leading to a much faster computation. The method is accurate even if the field to be evaluated is very close to the surface of a transducer. Results of Bessel beams, X waves, and focused Gaussian beams will be shown and compared with those obtained with the RSDF and the experiments. [This work was supported in part by Grant No. HL60301 from the National Institutes of Health of the U.S.A.]