A transient stagnation point numerical model was developed that includes gas-phase and solid-phase radiation and solid-phase coupling to describe the dynamic transition from a flame at higher stretch to a flame at lower stretch. To validate the model, low-stretch experiments using PMMA samples were performed in NASA Glenn's Zero Gravity Facility. When the final stretch rate is sufficiently low, the flame transitions to extinction. Above the critical stretch rate, the flame reaches a new steady state with larger flame standoff distance. But the transient process is very dynamic. The model captures the transient behavior of the experimental flame. A parametric study of the surface temperature and standoff distance demonstrates that the flame standoff overshoot at the beginning of the drop is the result of the faster response of the gas phase and the slower response of the solid layer immediate beneath the surface sample. The predicted surface energy balance shows that as the feedback from the flame decreases, the importance of the ongoing heat losses becomes greater, and extinction is observed when these losses represent 80% or more of the flame feedback. Extinction is attributable to insufficient heat feedback to the surface to compensate for existing heat losses under these low-stretch conditions. There is good agreement between the model and both the drop tower and previous buoyant low-stretch experiments in terms of a limiting stretch rate. This work supports the hypothesis that buoyant experiments with large burners can be used to evaluate the low-gravity, low-stretch flammability limits of a material. Published by Elsevier Inc. on behalf of The Combustion Institute.