We report on laser shock peening (LSP) of tungsten, a material used as a divertor in Tokamak machine for magnetic confinement fusion reactions such as the ITER facility (France) and JET facility (UK). Peak compressive stresses of -370 MPa and depths of up to 1.75 mm were recorded when 0.25 cm2 area of tungsten (99.95% pure) was irradiated by a 1030 nm Yb:YAG laser operating at 10 J, 10 ns. Furthermore, we demonstrate enhancement of compressive stresses in one direction, by application of circular polarised light in hard material like tungsten. However, no enhancement of compressive stresses with circular polarisation was observed in soft material like aluminium.