A system for limiting the size of a local storage of a processor is provided. A facility is provided in association with a processor for setting a local storage size limit. This facility is a privileged facility and can only be accessed by the operating system running on a control processor in the multiprocessor system or the associated processor itself. The operating system sets the value stored in the local storage limit register when the operating system initializes a context switch in the processor. When the processor accesses the local storage using a request address, the local storage address corresponding to the request address is compared against the local storage limit size value in order to determine if the local storage address, or a modulo of the local storage address, is used to access the local storage.