A method is provided for managing memory resources in a shared memory system. A point is identified (10) at which memory usage will be constrained. An object pertaining to an active user of the system is identified (20), and further objects related to this object are also found (30). A user memory footprint is then determined (40) from the footprints of the identified objects. Different constraint options are identified (50) and one of these is used to constrain (60) the user memory footprint. In this way the memory used by individual users may be tracked and constrained without having to place all the work from users into separate JVMs. Therefore the `bursty` nature of memory consumption by multiple users can be summed to result in a JVM which exhibits much less bursty memory requirements and allows individual users to have relatively relaxed constraints.