An aerodynamic fairing, made of a plastic material, for the outer laterally disposed longitudinally extending members, i.e., rocker panels, of bodies for passenger cars and utility-type motor vehicles, which, in conjunction with the outer wall of the longitudinal members, form a closed hollow body; in order to be able to extend a fairing of this type as far in the downward direction as is necessary for aerodynamic reasons, yet minimize the risk of damage to the fairing, the construction according to the present invention is such that the fairing comprises an upper zone, made of a plastic material which is comparatively dimensionally stable or form-rigid, and of a lower zone which can be elastically deformed and which is fastened to the upper zone in a preferably detachable manner, and in that the lower zone enables a reduction in its height in the event of contact with the ground by including predetermined flexing points or intentional bending places which facilitate such a height reduction.