We developed a method that accurately determines an unknown position of the high-intensity laser-pulse-material interaction site on the front side of a plate. It is based on interferometric measurements of a normal displacement at known positions on the plate’s rear side. The displacement is caused by reflections of various pulsed-laser-induced mechanical waves. We have superseded the long-established time-of-flight approach with the improved, triple-echo method. To accurately locate the origin of the laser-induced ultrasound on the plate with a known thickness, we only need to detect the arrivals of the first three consecutive mode unconverted waves. Our method works without knowing the propagation velocities of various ultrasonic waves and additionally solves some time-related drawbacks of the conventional time-of-flight approach. The relative uncertainty of the measured source-receiver separations obtained with the presented method is less than 0.01.