Propagation of one-dimensional “laminar” flame in combustible mixtures with spatially-periodic longitudinal velocity oscillations is investigated within the thermo-diffusive flame model using the large activation energy asymptotic technique. The ratio of the flame propagation velocity in the periodically disturbed versus undisturbed fieldsXis examined as a function of the amplitude parameter Γ for the complete range of wavelength parameter y (0, ∞). It is found that for infinitely longwave lengths γ →0 the dimensionless flame velocityXdecreases monotonically with Γ from unity towards zero without any extinction. For intermediate wavelengthsXfirst increases to a maximum value above unity and then decreases with Γ and eventually at a critical value Γ > Γebecomes less than unity as it continues to decrease towards zero. Therefore, for a given wavelength a critical amplitude of velocity oscillation is identified that results in a maximum burning velocity for the combustible mixture. In the limit of exceedingly short wavelengths γ →∞ the dimensionless velocityXis double valued function of Γ resulting in fast and slow burning flames. Also, a maximum critical value of amplitude Γeis predicted above which the flame will extinguish. Since planar flames do not experience any stretch by either flow divergence or curvature, the extinction is attributed to voluminal stretch introduced by Buckmaster. The predictions are found to be consistent with the prior experimental observations.