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When a laser beam of sufficient energy is incident on a medium, the absorption of the electromagnetic radiation leads to an increase of the local temperature. Due to thermal effects, displacements occur in the medium. These displacements can then propagate as elastic waves. Elastic waves can be separated into two components in a bulk: compression waves, corresponding to a curl-free propagation; and shear waves, corresponding to a divergence-free propagation \cite{aki2002quantitative}. Measures of the compression and shear waves are notably useful for inspecting solids such as a metal to reveal potential cracks or defects. defects \cite{Shan_1993}.  In biological tissues, induction of compression waves by laser has been studied with the development of photoacoustic imaging \cite{Xu_2006}, \cite{22442475}. Elastic waves used in photoacoustic imaging are typically of a few megahertz: at this frequency, in a soft tissue, shear waves are quickly attenuated, typically over a few microns, and only compression waves can propagate over a few centimeters. However, while induction of shear waves by laser in soft medium has never been shown - although  Li et al. has recently shown the possibility of the induction of surface acoustic waves by laser in soft medium \cite{Li_2012}, tissues  \cite{Li_2012}, \cite{Li_2014}, induction of shear waves by laser in soft medium has never been shown. .  This would yet be of interest for the shear wave elastography techniques. As its names indicates, this term covers the techniques used to measure or map the elastic properties of soft tissues using shear wave propagation \cite{muthupillai1995magnetic}, \cite{sandrin2002shear}. These techniques typically use low frequency (50-500 Hz) shear waves to observe their propagation over a few centimeters. 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 and of 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.