A snow sock is provided that includes a covering that extends in a circumferential direction. The covering has a thickness and an outer surface. A first thickness section is present and extends along a first arc length, and has a first thickness section inner surface that engages the outer surface of the covering. At least 50% of the first thickness section inner surface engages the outer surface of the covering and/or a first fill element. A second thickness section is also provided and is spaced from the first thickness section. The second thickness section extends in the circumferential direction along a second arc length, and has a second thickness section inner surface that engages the outer surface of the covering. At least 50% of the second thickness section inner surface engages the outer surface of the covering and/or a second fill element.