We study the propagation of elasto-plastic shockwaves induced by high power laser impacts in 2D polycrystalline metallic alloys in order to investigate the influence of the material microstructure on the fields of plastic strain and subsequent residual stresses. Implementing a visco-plastic constitutive relation at the grain scale accounting for two dislocation slip systems into a finite volume numerical scheme, simulations on single crystal specimens with different lattice orientations show that plastic strain is concentrated in narrow bands originating at the edges of the laser impact and parallel to the slip planes. In the case of polycrystalline microstructures composed of randomly oriented grains, it is found that the microstructure morphology is the origin of a heterogeneous distribution of the residual plastic strain and stress fields, which thus departs from the residual stress fields usually modelled when the microstructure is not accounted for. To account for the random character of polycrystal microstructures, we perform a statistical analysis of the mechanical fields over a large number of microstructures to quantify the dispersion of the results. It is found that even though the residual stresses induced by a laser impact are in compression on average at the center of the laser impact, some realizations of the microstructures can lead to localized concentrations of less compressive, or even tensile, residual stresses at the surface, thus probably reducing the fatigue resistance of the shocked material.