We present a unidimensional discrete solid-on-solid model evolving in time using a kinetic Monte Carlo method to simulate microstructuring of kerfs on metallic surfaces by means of laser-induced jet-chemical etching. The precise control of the passivation layer achieved by this technique is responsible for the high resolution of the structures. However, within a certain range of experimental parameters, the microstructuring of kerfs on stainless steel surfaces with a solution of H3PO4 shows periodic ripples, which are considered to originate from intrinsic dynamics. The model mimics a few of the various physical and chemical processes involved and within certain parameter ranges reproduces some morphological aspects of the structures, in particular ripple regimes. We analyze the range of values of laser beam power for the appearance of ripples in both experimental and simulated kerfs. The discrete model is an extension of one that has been used previously in the context of ion sputtering and is related to a noisy version of the Kuramoto-Sivashinsky equation used extensively in the field of pattern formation.