A differential quasi-one-dimensional flame model which accounts for flame curvature, lateral how expansion, and cross-stream diffusion is formulated. Expressions for the flame propagation speed (or displacement speed) are obtained by integration of the governing equations. The analysis shows that three mechanisms contribute to the enhancement of the displacement speed: a chemical mechanism associated with modifications to the reaction zone structure, lateral flow expansion, and cross-stream diffusion. An approach to study the sensitivity of the flame structure and propagation to curvature and strain rate is proposed based on the model formulation. In particular, a method for computing the curvature Markstein lengths from the solution of one-dimensional flames is described. Contributions to the Markstein length based on sensitivity analysis are shown to be associated primarily with processes in the reaction zone.