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This article presents the generation of elastic shear waves in a soft medium using a laser beam. Experiments show two different regimes depending on laser energy. Physical modelisation of the underlying phenomena reveal a thermoelastic regime due to a local dilatation resulting from temperature increase; And an ablative regime due to a partial vaporization of the medium by the laser. Theoretical displacements are close to experimental measurements. A numerical study based on the physical modelisation gives comparable propagation pattern patterns  as in experiments. experimental ones.  These results give a physical basis on the feasability of a shear wave elastography technique using a laser beam.