Many recently proposed BigData processing frameworks make programming easier, but typically expect the datasets to fit in the memory of either a single multicore machine or a cluster of multicore machines. When this assumption does not hold, these frameworks fail. We introduce the InfiniMem framework that enables size oblivious processing of large collections of objects that do not fit in memory by making them disk-resident. InfiniMem is easy to program with: the user just indicates the large collections of objects that are to be made diskresident, while InfiniMem transparently handles their I/O management. The InfiniMem library can manage a very large number of objects in a uniform manner, even though the objects have different characteristics and relationships which, when processed, give rise to a wide range of access patterns requiring different organizations of data on the disk. We demonstrate the ease of programming and versatility of InfiniMem with 3 different probabilistic analytics algorithms, 3 different graph processing size oblivious frameworks; they require minimal effort, 6–9 additional lines of code. We show that InfiniMem can successfully generate a mesh with 7.5 million nodes and 300 million edges (4.5GB on disk) in 40min and it performs the PageRank computation on a 14GB graph with 134 million vertices and 805 million edges at 14 min per iteration on an 8-core machine with 8GB RAM. Many graph generators and processing frameworks cannot handle such large graphs. We also exploit InfiniMem on a cluster to scale-up an object-based DSM.