This work advances on the application of discrete models to the simulation and understanding of pattern formation occurring in microstructuring techniques. The main issue of this thesis are ripples appearing in kerfs (grooves) structured on metallic surfaces by laser-induced jet-chemical etching (LJE). The LJE experiment is a far from equilibrium system and is composed by various chemical and physical processes with non-linear interactions, which is the typical scenario for emergence of patterns. We propose a minimal phenomenological representation of the dynamics by the interplay of two mechanisms: curvature-dependent erosion and thermally-activated surface diffusion. The LJE simulation is a discrete solid-on-solid model evolved in time using a kinetic Monte-Carlo method. The simulation allows to represent the main parameters of the system in a probabilistic sense, and reproduces qualitatively the ripple regimes appearing in the LJE experiment.