This paper proposes a mode domain beamforming method for a 3 × 3 uniform rectangular array of two-dimensional (2D) acoustic vector sensors with inter-sensor spacing much smaller than the wavelengths in the working frequency band. The acoustic modes are extracted from the particle velocity observations in light of the source-sink pictures of the Taylor's series multipoles [Wikswo and Swinney, J. Appl. Phys. 56(11), 3039-3049 (1984)]. Then, similar to other mode domain methods, the modes are synthesized to obtain the desired beam pattern. The proposed method is limited to the cases where five is the maximum order of the modes for pattern synthesis, meaning that the directivity index in the 2D isotropic noise case can reach up to 10.4 dB. The proposed method has been validated by field experiments.