The aim of this paper is to develop a model allowing a fast first approximate estimation of the elastic–plastic stress wave propagation caused by a laser impact and the resulting residual stress field. We start by modeling the stress wave propagation, adopting a 1D uniaxial modeling, reducing the behavior of the specimen to the axis of the laser impact, excluding any edge effects caused by the edges of the laser spot. The plastic strain field resulting from this propagation can in turn be used to compute the residual stresses, by making use of an analytic modeling in the case of an infinite planar plate. The accuracy of the 1D model is assessed by comparing it to finite elements simulations, acting as a reference solution, for several materials and laser spot diameters. The results show that the stress wave propagation from the 1D model is close to identical to the reference solution. The residual plastic and stress fields from the finite elements model present a uniaxial distribution on a large portion of the laser spot, except for the very edge and spot center. The comparison between the 1D model and the reference solution shows a good match, indicating that the 1D model can be used for a fast approximation the mechanical fields created by a laser impact for laser spot diameters larger than 2 mm.