An analytical model is developed to study the combustion response of turbulent premixed flames to acoustic oscillations. The analysis is based on a level-set flamelet model, and accommodates spatial variations in chamber geometry and mean-flow properties. All known factors affecting the flame response to local flow disturbances are analyzed. A triple decomposition technique, which expresses each flow variable as the sum of a long-time-averaged, a periodic, and a turbulent component, is used to examine the interactions between acoustic and turbulent motions and their collective influence on the flame dynamics. As specific examples, both a simple and an enveloped flame commonly observed in a swirl-stabilized combustor are studied. The resultant flame response is incorporated into a three-dimensional acoustic analysis to determine the stability characteristics of a model gas-turbine combustor. Results are consistent with experimental observations and numerical simulations in terms of the stability boundary and acoustic wave properties. In particular, the enveloped flame tends to be resonantly coupled with the acoustic velocity oscillation, leading to large excursions of combustion oscillations.