The main purpose of this PhD project is to develop an ultrasonic method for 3D vector flow imaging. The motivation is to advance the field of velocity estimation in ultrasound, which plays an important role in the clinic. The velocity of blood has components in all three spatial dimensions, yet conventional methods can estimate only the axial component. Several approaches for 3D vector velocity estimation have been suggested, but none of these methods have so far produced convincing in vivo results nor have they been adopted by commercial manufacturers. The basis for this project is the Transverse Oscillation (TO) method, which estimates both the axial and the lateral velocity components. The first part of the scientific contribution demonstrates that a commercial implementation of the TO method is feasible. Afterwards, the method is expanded to a phased array geometry, and performance metrics based on the TO fields are suggested. They can be used to optimize the TO method. In the third part, a TO method for 3D vector velocity estimation is proposed. It employs a 2D phased array transducer and decouples the velocity estimation into three velocity components, which are estimated simultaneously based on 5:1 parallel receive beamforming. Simulation results demonstrate the feasibility of the method. In the final part, an experimental investigation of the 3D TO method is presented. Velocity measurements of steady flow were conducted in a flow-rig system, and the data were acquired using an experimental ultrasound scanner and a 2D transducer. The three velocity components along the center line are measured with relative (to the expected values) biases and standard deviations lower than 5 % and 12 %, respectively. At the center of the vessel, the mean and standard deviation of 100 estimated velocity vectors are (vx, vy, vz) = (-0.03, 95, 1.0) ± (9, 6, 1) cm/s compared with the expected (0, 96, 0) cm/s. Afterwards, 3D vector flow images from a cross-sectional plane of the vessel are presented. The out of plane velocities exhibit the expected 2D circular-symmetric parabolic shape. The experimental results verify that the 3D TO method estimates the complete 3D velocity vectors, and that the method is suitable for 3D vector flow imaging.