The invention relates to encapsulating partitioned timed media data to be streamed to a client's device, the partitioned timed media data comprising timed samples, each comprising a plurality of subsamples. After having grouped several of the subsamples to form at least one group so that at least part of the subsamples belongs to a group of subsamples, at least two subsamples of the same group are selected from amongst the plurality of subsamples of one of the timed samples and at least one track comprising the selected subsamples is created. Next, for the at least one created track, one sub-track box is created for each of the subsamples selected to create the at least one track, at least one of the created sub-track boxes comprising definitions and properties that are common to the selected sub-samples. Each of the created tracks is independently encapsulated in at least one media file.