Flame structure and ignition and extinction processes associated with a strained fuel strip are explored numerically using detailed transport and complex kinetics for a propane-air reaction. Ignition modes are identified that are similar to those predicted by one-step activation energy asymptotics, i.e., modes in which diffusion dames can ignite as independent or dependent interfaces and modes in which single premixed or partially premixed flames ignite and burn. These ignition modes have been found to be dependent on critical combinations of strain rate, fuel strip thickness and initial reactant temperatures. The formation of NO/NO2 is found to be strongly dependent on strain rate and the local molecular mixing of reactants which occurs as a consequence of strain. Extinction in this configuration is seen to occur due to fuel consumption by adjacent flames, although viscosity is seen to have the effect of delaying extinction by reducing the effective strain rate experienced by the flames. Response of the flames to oscillatory strain rates is seen to be strongly dependent on the amplitude and frequency of the oscillation.