A fully nonlinear evolution equation governing the propagation of a premixed flame through a large-scale spatially periodic shear flow is derived, and steady-state solutions are obtained numerically. The gas density is assumed to be constant across the flame, but the local normal burning speed is allowed to vary with the local strain and curvature along the flame front in order to investigate the influence of the length scale of the external flow on the average propagation speed of the wrinkled flame. At fixed values of the amplitude of the flow-field variations an increase in the length scale (relative to the flame thickness) is found to result in an increase in the average flame propagation speed, in accordance with the predictions of earlier theoretical investigations and with experimental observations for the regime of large-scale turbulence. The propagation speed of the wrinkled flame is calculated to exhibit the experimentally observed bending effect, the tendency of the rate of change of the burning velocity to decrease with increasing turbulence intensity at low fixed turbulence Reynolds numbers. It is shown also how the average flame speed depends on the ratio of the transverse to longitudinal length scale associated with the periodic flow.