Abstract: Reconstruction of the three-dimensional fluid velocity vector field in a moving medium from a set of measurements of the acoustic propagation time between a multiplicity of transmitter and receiver locations on a stationary boundary surface. The inversion of the integrals relating the acoustic propagation path to the propagation time measurements is effected by linearization and discrete approximation of the integrals and application of an algebraic reconstruction technique (ART). The result of the process is to obtain the X, Y, and Z components of the fluid velocity vector at every point within a region bounded by a surface containing the acoustic transducers. Since this technique does not require the presence of scattering centers or the optical transparency of the medium, it may be applied in many cases (i.e., turbid, opaque, or chemically pure media) where Doppler or optical (e.g., laser holography) methods fail.