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This article presents describes  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 modeling  of the underlying phenomena reveals 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 Computed theoretical  displacements are close to experimental measurements. A numerical study based on the physical modelisation modeling  gives comparable propagation patterns as experimental ones. These results give provide  a physical basis on the feasability of a shear wave elastography technique using a laser beam.