A case for a mobile device with a screen, the case comprising a band arranged to surround the edge of the device. The band comprises a layer of flexible polymer (1) and a layer of a damping material (3) which is softer than the flexible polymer provided within the flexible polymer layer. The damping material (3) has a plurality of protrusions (2) projecting inwardly from a substantial portion of the inner periphery of the band to engage with the device. The protrusions are arranged such that, in normal use there is substantially no contact between the band and the device other than through the protrusions.