The extinction of lean limit methane-air flames was experimentally studied in a vertical variable-geometry flammability tube with rectangular cross section. Four tube configurations have been investigated: 50 × 50, 100 × 100, 200 × 200, and 20 × 200 mm, using schlieren photography, visual observation, measurement of heat flux to the wall, and image intensifier photography. Extinction of the lean limit flame which did not involve unstable flame fluctuations occurred only for upward propagation in the tube sizes 50 × 50 and 100 × 100 mm. In all the other tube geometries, the extinction was preceded by unstable flame motions. The flow field characteristics ahead of the flame for an upward propagating flame have been calculated numerically using a finite difference method. The results were applied to the determination of flame stretch. The comparison of the theoretically calculated Karlovitz number and the experimental observations suggest that flame stretch is the primary mechanism of extinction in the flammability tube when the flame is stable prior to extinction. Preferential diffusivity was found to have significant effects on the lean limit flame behavior. Preferential diffusion ahead of the flame lowered the lean limits in smaller tubes and caused cellular structures to appear in larger tubes.