A mathematical model is developed describing the natural smoldering of logs. It is considered the steady one dimensional propagation of infinitesimally thin fronts of drying, pyrolysis, and char oxidation in a horizontal semi-infinite log. Expressions for the burn rates, distribution profiles of temperature, and positions of the drying, pyrolysis, and smoldering fronts are obtained in terms of the smolder temperatures. An appropriate smolder transfer number is defined. Heat transfer by conduction, convection, and radiation inside the porous matrix of the log is considered, as are convection and radiation around the log and inside the boundary layer adjacent to the smoldering end. Solutions for the problem without circumferential heat losses and for a single front of drying and pyrolysis are also presented. The effects of variations of several parameters, such as moisture content, log diameter, pyrolysis temperature, heat of char oxidation, heat of pyrolysis, porosity, fuel density, and char density, are evaluated. The theoretical burning rates are in good agreement with available experimental data.