The concepts of fire line rotation and fire line extension are introduced as a complement to the usual rate of spread to describe the movement of surface fires. It is shown that both rotation and translation of the fire line elements contribute to increasing their length and reducing the curvature of the fire line. It is shown that in the case when the wind velocity is not parallel to the rate of spread vector, the transverse convective flux along the fire front induces a change of the rate of spread and consequently a rotation movement of the fire line. Using empirical formulations for the dependence of the rate of spread on wind velocity, a model for the rotational velocity of a wind and slope driven fire front is developed. The model is compared with experimental laboratory results for wind- and slope-induced extension and rotation of linear fire fronts.