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In this article, we study thus the generation of shear waves by a laser beam in a soft medium. We describe theoretically the two regimes occurring at different laser energies. We propose then a physical model to describe the observed phenomena, which is compared quantitatively and qualitatively with the experimental results.  In our experiment, illustrated by Figure \ref{Figure1}, a Q-switch Nd:YAG laser (EverGreen 200, Quantel, Les Ulis, France) produced a 10 ns pulse of 10 to 200 mJ energy at a central wavelength of 532 nm in a 5 mm diameter circular beam. The laser beam was absorbed in a 4x8x8 cm$^3$ tissue-mimicking black mat phantom made of water andof  5\% polyvinyl alcohol and 1 \% black graphite powder. Two freezing/thawing cycles were applied to stiffen the material to a value of 25$\pm$5 kPa \cite{17375819}. To observe the resulting shear waves, the medium was scanned simultaneously with a 5 MHz ultrasonic probe made of 128 elements connected to a Verasonics scanner (Verasonics V-1, Redmond, WA, USA). The probe was used in ultrafast mode \cite{bercoff2004supersonic}, acquiring 4000 ultrasound images per second during 30 ms. Due to the presence of graphite particles, the medium presented a speckle pattern on the ultrasound image: tracking the speckle spots with an optical flow technique (Lucas-Kanade method with a 64x5 pixels window) enabled to compute displacement along ultrasound axis. Displacements along time were finally filtered from 200 to 800 Hz using a 5th order Butterworth filter. In this setup, Z was defined as the laser beam axis and origin of coordinates (0,0,0) as the laser impact location on the medium.