The tires for vehicles possess under their tread a belt which extends in the circumferential direction. At least one, preferentially two, layers contain, as strengthening and stabilizing means, foils or sheets with direction-dependent rigidity, which possesses its highest value in a preferred direction. The foils or sheets are so arranged that the preferred direction is oblique to the circumferential direction. Preferentially, the direction-dependent rigidity is realized with a waving or crimping. Through this alignment, which is arranged oblique to the tire circumference, the stabilizing effect of the waving is seen in both the longitudinal as well as the oblique directions. Thus, in comparison with the usual belted tires, less material is needed in tire production, and these tires are both light, but nevertheless possess good driving characteristics and superb rolling resistance.