A physicomathematical model is proposed for the phenomenon of formation of periodic striations in oxygen laser cutting of mild steel sheets. The mechanism of roughness origination is assumed to be caused by a cyclic reaction of iron–oxygen oxidation. The mathematical description is based on solving the adjoint problems of heat and mass transfer in the liquid phase and in the solid metal with nonlinear moving interfaces between the substances and phase changes. The motion of the boundaries occurs owing to metal melting under the action of focused laser radiation and the heterogeneous chemical reaction of iron oxidation in oxygen. The main feature of iron oxidation is the loss of protective properties of its oxide film due to melting. The general statement of the problem for the nonlinear heat-conduction equation with variable coefficients is formulated by the type of the Stefan problem solved with the use of the difference method with smoothing coefficients at the melting point and the fictitious domain method, which allows obtaining of the solution without explicit identification of the cut boundary and the phase-transition front. Results of numerical simulations of the shape and linear size of roughness as functions of the cutting velocity, purity of oxygen and thickness of the film of the iron oxide being formed are presented.