A steady-state jet model is developed to simulate combustion of iron rods in a high-pressure oxygen atmosphere. The suggested jet mode of combustion is characterized by a constant regression rate of melting interface (RRMI) with its value solely controlled by a melting droplet area between the melting front and the maximum temperature region; experimentally observed periodic droplet detachment does not affect RRMI. An analytical solution in an adiabatic approach and a numerical solution with radiative losses are obtained. The developed model comprises two parameters that simulate mass and heat transfer. The analytical solution contains the product of these coefficients. By analyzing the results of experiments with 1-mm diameter rods, the values of these coefficients were obtained by means of an optimization procedure. The simulation predictions are in agreement with experimental data for different rod diameters and oxygen pressures.