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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 in the local temperature. Due to thermal effects, displacements occur in the medium, which can then propagate as elastic waves. Elastic waves within a bulk can be separated into two components: compression waves, corresponding to a curl-free propagation, and shear waves, corresponding to a divergence-free propagation \cite{aki2002quantitative}. Notably, measures of the transmission characteristics of compression and shear waves are useful for inspecting solids, such as a metal, to reveal potential cracks or 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, shear waves are quickly attenuated in soft tissues, typically over a few microns, and only compression waves can propagate over a few centimeters.  While the induction of surface acoustic waves by laser in soft tissues was recently demonstrated by Li et al. \cite{Li_2012}, \cite{Li_2014}, a similar phenomenon with shear waves in bulk medium has never been described. This is of great interest for thedevelopment of laser-based  shear wave elastography techniques. technique.  As its name indicates, shear wave elastography comprises the techniques used to map the elastic properties of soft tissues media  using shear wave propagation \cite{Plewes_1995}, \cite{muthupillai1995magnetic}, \cite{Catheline_1999}. These techniques typically use low frequency (50-500 Hz) shear waves so that their propagation can be observed over a few centimeters. These techniques currently use an external shaker or a focused acoustic wave to induce the shear wave. These two methods are however limited in some situations, such as the brain which is protected by the skull or intravascular imaging because of the small size of the blood vessels, so alternative shear wave generation methods have been explored recently. Among these methods some researchers proposed to use natural motion of the medium \cite{Hirsch_2012}, \cite{Weaver_2012}, \cite{Zorgani_2015}, the Lorentz force \cite{Basford_2005}, \cite{Grasland_Mongrain_2014}, \cite{Grasland_Mongrain_2016} or electrolysed-induced bubbles \cite{Montalescot_2016}. Compared to all these generation methods, a laser presents the advantages of being fully remote, without need of coupling gel or similar; and the source can be miniaturized at low cost using a fiber optics, so shear waves can be induced very close to the studied medium.  In this article, we study the generation of shear waves by a laser beam in a soft medium. We theoretically describe the resulting two regimes observed to occur at different laser energies. We then propose a physical model to describe the observed phenomena, which is compared quantitatively and qualitatively with the experimental results.