The aim of the paper is to get insight into flow patterns visualized by suspended anisotropic reflective particles. The motion of triaxial ellipsoids embedded in a three-dimensional flow, i.e., which cannot be reduced to a local plane Couette flow, is calculated. Both the asymptotic trajectory and the transient time to reach it are discussed. These results are used to simulate laser sheet visualizations of two classical three-dimensional flows (Taylor–Couette vortices and flow between rotating disks) where the particle history is shown to be negligible. The simulated visualizations are well compared to experimental ones but the paper addresses the fact that the legitimate question of what shows the visualization does not have a simple answer. Nevertheless, these results open the way for quantitative comparisons between computational fluid dynamics and experimental visualizations. ©1998 American Institute of Physics.