In this paper, we study the problem of source coding with Massive Random Access (MRA). A set of correlated sources is encoded once for all and stored on a server while a large number of clients access various subsets of these sources. Due to the number of concurrent requests, the server is only able to extract a bitstream from the stored data: no re-encoding can be performed before the transmission of the data requested by the clients. First, we formally define the MRA framework and propose to model the constraints on the way subsets of sources may be accessed by a navigation graph. We introduce both storage and transmission costs to characterize the performance of MRA. We then propose an Incremental coding Based Extractable Compression (IBEC) scheme. We first show that this scheme is optimal in terms of achievable storage and transmission costs. Second, we propose a practical implementation of our IBEC scheme based on rate-compatible LDPC codes. Experimental results show that our IBEC scheme can almost reach the same transmission costs as in traditional point-to-point source coding schemes, while having a reasonable overhead in terms of storage cost.