This article presents a simple model to describe the smoldering combustion of a thin solid burning in a narrow gap. Smoldering front under such a condition is unstable because of a similar instability mechanism to gaseous premixed combustion and produces a fingering pattern. In the present model, the Lewis number, defined as the ratio of the solid thermal diffusivity to the oxygen diffusivity, is typically less than 0.1, while the Lewis number of gaseous premixed flame is generally close to unity. It was found that the propagation speed increases with a decrease in the Lewis number, the opposite trend to the one-dimensional propagation. The fingering pattern predicted for Le = 0.1 shows, similarly to experimental observations, repeated processes of the split of a smoldering front into two branches and the subsequent extinction of one of the split branches.