We investigate the use of maximum distance separable (MDS) codes to cache popular content to reduce the download delay of wireless content delivery. In particular, we consider a cellular system where devices roam in an out of a cell according to a Poisson random process. Popular content is cached in a limited number of the mobile devices using an MDS code and can be downloaded from the mobile devices using device-to-device communication. We derive an analytical expression for the delay incurred in downloading content from the wireless network and show that distributed caching using MDS codes can dramatically reduce the download delay with respect to the scenario where content is always downloaded from the base station and to the case of uncoded distributed caching.