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A method of ultrasonic three-dimensional (3-D) vector velocimetry, which is derived by extending the previously proposed two-dimensional (2-D) vector velocimetry, is presented. In the proposed method, the three vector components of velocity to be measured are defined as the velocity in the beam axial direction, and angle velocities in two transverse directions. To derive the three components of velocity, signals detected by a 2-D array transducer are first 2-D Fourier transformed in the spatial domain parallel to the 2-D array transducer and then are one-dimensional (1-D) Fourier transformed in the time domain. The advantage of the proposed method is that it uses a linear signal processing, so it can simultaneously measure individual velocities of multiple scatterers. Computer simulations clearly demonstrate the effectiveness of the proposed method.